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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,518

Hi bobbym,

The solutions #4532 and #4533 are correct. Marvelous!

#4534. If

, find the value of .#4535. Find the value of

Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,164

Hi;

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,518

Hi bobbym,

The solutions #4534 and #4535 are correct. Excellent!

#4536. If

, find the value of .#4537. If

, find the value of .Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,164

Hi;

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,518

Hi bobbym,

The solutions #4536 and #4537 are correct. Good work!

#4538. Find the value of

.#4539. Find the value of

.Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,164

Hi;

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,518

Hi bobbym,

The solutions #4538 and #4539 are correct. Neat work!

#4540. Find the value of

.#4541. If for an angle

, , then find the value of .Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,164

Hi ganesh;

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,518

Hi bobbym,

The solutions #4540 and #4541 are correct. Brilliant!

#4541. Find the value of

.#4542.

Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,164

Hi;

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,518

Hi bobbym,

The solutions #4541 and #4542 are correct. Neat work!

#4543. Find the value of

.#4544. Find the value of

.Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,164

Hi ganesh;

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,518

Hi bobbym,

The solutions #4543 and #4544 are correct. Good work!

#4545. If θ is an acute angle and sec θ = 13/12, then find the value of tan θ.

#4546. If cos θ = 1/2, find the value of cosec[sup]2[/sup] θ.

Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,164

Hi ganesh;

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,518

Hi bobbym,

The solution #4545 is correct. Neat work!

The solution

#4547. In any triangle ABC, find the value of sin{(B + C)/2}.

#4548. If sec θ + tan θ = m and sec θ - tan θ = n, then find the value of mn.

Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,164

Hi;

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,518

Hi bobbym,

The solutions #4547 and #4548 are correct. Stupendous!

#4549. If cos θ = x and cosec θ = y, find cot θ.

#4550. Find the value of

.Character is who you are when no one is looking.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,518

Hi bobbym,

#4551. If

, find θ.#4552. If

, find θ.Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,164

Hi;

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,518

Hi bobbym,

The solutions #4551 and #4552 are correct. Neat work!

#4553. The angle of elevation of the top of a tower from a point at a distance of 100 meters from the base of the tower is found to be 45 degrees. Find the height of the tower.

#4554. Find the angle of elevation of the top of a tower, whose height is 100 meters, at a point whose distance from the base of the tower is 100 meters.

Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,164

Hi;

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,518

Hi bobbym,

The solutions #4553 and #4554 are correct. Good work!

#4555. If the angle of elevation of the Sun is 60 degrees, then find the ratio of the height of a tree with its shadow.

#4556. From the top of a 10 meter high tower, the angle of depression of a point on the ground is found to be 30 degrees. Find the distance of the point from the base of the tower.

Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,164

Hi;

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,518

Hi bobbym,

The solution #4555 is correct. Good work!

#4557. Find the value of x is

.#4558.

Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,164

Hi ganesh;

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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