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Level of Difficulty  III Questions.1. If the sides of a triangle are in Arithmetic Progression, then find the value of in terms of . 2. A circle is inscribed in an equilateral triangle of side a. Find the area of the square inscribed in this circle. 3. Find the general value of θ satisfying the equation tan^{2}θ + sec2θ = 1. 4. Solve the equation sin x  3sin 2x + sin 3x = cos x  3cos 2x + cos 3x. Character is who you are when no one is looking. #2 20090315 23:43:26
Re: Level of Difficulty  III Questions.5. Find the area bounded by the curve x^{2}=4y and the 7. If a>0, b>0, and c>0, prove that . 8.Find the equations of straight lines passing through (2, 7) and having an interept of length 3 between the striaght lines 4x+3y = 12 and 4x+3y = 3. Character is who you are when no one is looking. #3 20090316 03:42:32#4 20090316 05:13:59
Re: Level of Difficulty  III Questions.Answer to 7: Character is who you are when no one is looking. #5 20090317 02:06:18
Re: Level of Difficulty  III Questions.9. For what values of m does the system of equations Character is who you are when no one is looking. #6 20090414 04:25:37
Re: Level of Difficulty  III Questions.Hi Ganesh; After a lot of algebraic thrashing and some trial and error: These values of m satisfy the constraints x>0 and y>0 Last edited by bobbym (20090414 04:38:13) In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #7 20090421 13:35:26
Re: Level of Difficulty  III Questions.#1: tan(A/2) +tan(C/2) = (2/3)cot(B/2) #8 20090421 14:56:34
Re: Level of Difficulty  III Questions.#6 : cosC=1/2⇒b² (b/2)²=c² (ab/2)² ⇒ab=a²+b²c² ⇒3ab=(a+b)² c²a+b+c)(a+bc)a+b+c)(a+b+c2c)= #9 20090421 20:44:35
Re: Level of Difficulty  III Questions.Hi bitus, doesn't work when I plug it in. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #10 20100517 17:26:06
Re: Level of Difficulty  III Questions.1.from sine rule we get sinA+sinC=2sinB, or cos([AC]/2)=2cos(B/2) Last edited by BO (20100517 17:32:48) #12 20100522 01:03:22
Re: Level of Difficulty  III Questions.
Last edited by irspow (20100522 01:04:34) #13 20100522 22:34:14
Re: Level of Difficulty  III Questions.Well done, Character is who you are when no one is looking. 