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Trigonometry : Truly difficult Practice Questions. . .

hemang

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8 Sep 2011 12:21:58 IST

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8 Sep 2011 12:21:58 IST

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Trigonometry : Truly difficult Practice Questions. . .

AIEEE , BITSAT , IIT JEE , KCET (Engg) , MANIPAL UGET (Engg) , SCRA , TANCET , UPSEE , VITEEE , VITMEE , academic , Maths

these are too good question. remember to rate me if you like these. :-)

Q) If $a$ and $b$ are positive integers such that

$\sqrt{8+\sqrt{32+\sqrt{768}}}=a\cos{\frac{\pi}{b}}$ ,

compute the ordered pair $(a,b)$ .

Q) Find y :

$\frac{4cos^2(y)cos(3y) + 8cos(y)\sqrt{cos(y)} + 6cos(y)cos(2y) + 14\sqrt{cos(y)} + 16}{8cos(y)cos(5y) + 22\sqrt{cos(y)} + cos...$

Q) Find the value of $A$
$csc\frac{\pi}{32}+csc\frac{\pi}{16}+csc\frac{\pi}{8}+csc\frac{\pi}{4}+csc\frac{\pi}{2}=cotA\pi$

Q) Prove that
$\tan{\frac{2\pi}{13}}+4\sin{\frac{6\pi}{13}}=\sqrt{13+2\sqrt{13}}$

Q) Prove that if $0<x<\pi/2$ , then $\sec^6 x+\csc^6 x+(\sec^6 x)(\csc^6 x)\geq 80$ .

Q) Calculate
$tan \left(\frac{3 \pi}{11}\right)+ 4sin\left(\frac{2\pi}{11}\right)$

Q) evaluate :

$cos(\frac{\pi}{7}) + cos(\frac{2\pi}{7}) + ....... + cos(\frac{6\pi}{7})$

Q) evaluate :

$\sqrt[3]{\cos(\frac{2\pi}{7})}+\sqrt[3]{\cos(\frac{4\pi}{7})}+\sqrt[3]{\cos(\frac{8\pi}{7})}=?$

Q) Solve the equation $\sin 5x + \cos 5x = cos 13x$

Q) Evaluate: $4\cos 18^{\circ}-3\sec 18^{\circ}-2\tan 18^{\circ}$

Q) solve for x $(cosx)^n-(sinx)^n=1,$ where $n\in \mathbb {N}$ .

Q) Find the value of:

$cos\left ( \frac{2\pi}{13} \right ) + cos\left ( \frac{6\pi}{13} \right ) + cos\left ( \frac{8\pi}{13} \right )$

Prove that :

$\cos \frac{\pi}{2005} + \cos \frac{3\pi}{2005} + \cos \frac{5\pi}{2005} + \ldots + \cos \frac{2003 \pi}{2005} = \frac{1}{2}$

Q) $(1+tan 1^\circ)(1+tan 2^\circ)(1+tan 3^\circ)....(1+tan 45^\circ)=2^n,$ find $n.$

Prove that $\sin{1^\circ}+\cos{1^\circ}\notin\mathb{Q}$ .

here Q stands for the set of rational numbers.

source : www.artofproblemsolving.com

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Comments (2)

darshana bhagat

New kid on the Block

Joined: 21 Aug 2011 22:33:58 IST

Posts: 4

10 Sep 2011 11:48:31 IST

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these are really good questions. do u have answers of these

alok vats

Hot goIITian

Joined: 1 Jun 2011 05:26:27 IST

Posts: 178

11 Sep 2011 17:32:57 IST

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Yeah !! do u have answers of these questionzz ;-)

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