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#1 Re: Help Me ! » sin18 » 2007-03-31 20:09:41

dear affirmation;

if you look carefully you will see this

if x=18 so cos3x=sin2x

=cos2x.cosx-sin2x.sinx=2sinx.cosx

=cos2x.cosx-2sin^2.cosx=2sinx.cosx

=cos2x-2sin^2=2sinx
=1-2sin^2-2sin^2=2sinx

=4sin^2+2sinx-1=0
so Δ=2√5
then sinx=(√5-1)\4  sinx=(√5+1)\4   second value doesn't provide the equation

so true value is sin18=(√5-1)\4

#2 Re: Exercises » Trignometry Ex.1 » 2007-03-30 23:11:13

now dear ganesh please solve this

cos2∏\11+cos4∏\11+cos6∏\11+cos8∏\11+cos10∏\11=?

the value is a rational

#3 Re: Exercises » Trignometry Ex.1 » 2007-03-30 23:06:14

tan.tan=(sin.sin)\(cos.cos)

tan.tan.cos=(sin.sin)\(cos.cos)\cos
=(sin.sin)\cos
=(sin\cos).sin
=tan.sin

#4 Re: Exercises » Trignometry Ex.1 » 2007-03-30 23:03:50

if tan.cot=1

(1-tan)\(1+tan)=(cot-1)\(cot+1)

cot+1-tan.cot-tan=cot-1+tan.cot-tan

so 1-tan.cot=tan.cot-1

2=2tan.cot
tan.cot=1

#5 Re: Exercises » Trignometry Ex.1 » 2007-03-30 22:56:59

(sin+cos)\(sin-cos)=[(sin\cos)+1]\[(sin\cos)-1]

=[(sin+cos)\cos]\[(sin-cos)\cos]
=(sin+cos)\(sin-cos)

so (sin+cos)\(sin-cos)=(sin+cos)\(sin-cos)

#6 Re: Exercises » Trignometry Ex.1 » 2007-03-30 22:53:07

the value of sixth question is 1/7

#7 Re: Exercises » Trignometry Ex.1 » 2007-03-30 22:51:28

the value of fifth question is 17/19

#8 Re: Exercises » Trignometry Ex.1 » 2007-03-30 22:50:17

the value of forth question is 1/7

#9 Re: Exercises » Trignometry Ex.1 » 2007-03-30 22:49:12

value of third question is -9/7

#10 Re: Exercises » Trignometry Ex.1 » 2007-03-30 22:47:31

the value of second question is 1

#11 Re: Exercises » Trignometry Ex.1 » 2007-03-30 22:11:52

if sinA=5/13 so cosA=12/13 then sinA/cosA=tanA (5/13)/(12/13)=5/12=tanA

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