Trigonometric Ratios of Multiples of an Angle

Q.

What is the formula of $\cos 3\theta$?

Q. If Tn=sin^n x + cos^n x, prove that- T3 - T5/T1 = T5 - T7/T3

Q.

If $\sin A=\sin B$ and $\cos A=\cos B$, then

A.$\sin \frac{A-B}{2}=0$

B.$\sin \frac{A+B}{2}=0$

C.$\cos \frac{A-B}{2}=0$

Q.

Prove that $co{s}^{2}X+co{s}^2(X+\frac{\pi }{3})+co{s}^2(X-\frac{\pi }{3})+co{s}^2=\frac{3}{2}.$

Q. sin(sin inverse 3π/11 + cos inverse x) = 1, then x is A)-3π/11 B)π/2-3π/11 C)3π/11 D)8π/11

Q. sin inverse x + cos inverse (1-x)=sin inverse (-x)

Q. 42. sin A / (cot A + cosec A) = 2 + sin A / (cot A - cosec A)

Q.

If $ta{n}^{2}A=2ta{n}^{2}B+1$ then the value of $cos2A+si{n}^{2}B$.

__

Q.

Prove that cos A 2A cos 4A cos 8A = $\frac{sin16A}{16sinA}$.

Q.

Prove that $\frac{sec8\theta -1}{sec4\theta -1}=\frac{tan8\theta }{tan2\theta }$

Q.

Prove the following:
$\frac{\text{sin x - sin 3x}}{\text{cos x + cos 3x}}=\text{tan 2x}$

Q.

If R denotes circum radius, then, in $△ABC,\frac{b^2-c^2}{2aR}$ is equal to

1. sin(B-C)

2. cos(B-C)

3. None of these

4. cos B - cos C

Q.

Prove that:

sin x + sin 3x +sin 5x + sin 7x = 4 cos x cos 2x sin 4x

Q. Sin(A + B) = SinACosB + CosASinB

Q.

If tan $\frac{A}{2}$ = $\frac{3}{2}$, then $\frac{1+cosA}{1-cosA}$ =

1. -5

2. 5

3. 9/4

4. 4/9

Q. If $\alpha \in [\frac{\pi }{2},\pi ],$ then the value of $\sqrt{1+\sin \alpha }-\sqrt{1-\sin \alpha }$ is

1. $2\cos \frac{\alpha }{2}$
2. $2\sin \frac{\alpha }{2}$
3. $2$
4. $2\tan \frac{\alpha }{2}$

Q. The domain of the function f(x) = sin–1 (sin 2x) is

Q. If Pn = cos^n theta + sin^n theta Maximum value of P1000 will be

Q.

Prove the following:
$\frac{\text{sin 5x + sin 3x}}{\text{cos 5x + cos 3x}}=\text{tan 4x}$

Q.

sinA + cosA =

1. 

2. 

3. 

4. 

Q.

The roots of $(2-2i{)}^{\frac{1}{3}}$

1. 

2. None of the above

3. 

4. 

Q. If $8{\sin }^2\theta +10\sin \theta \cos \theta -3{\cos }^2\theta =0$ then $\theta =$

1. 
2. 
3. 
4. 

Q.

If $tanx+tan(x+\frac{\pi }{3})+tan(x+\frac{2\pi }{3})=3,$ prove that $\frac{3tanx-ta{n}^{3}x}{1-3ta{n}^{2}x=1.}$

Or

If $sin\theta =nsin(\theta +2\alpha ),$ prove that $tan(\theta +\alpha )=\frac{1+n}{1-n}tan\alpha .$

Q.

cosec A - 2cot 2A cos A =

1. 2sinA

2. secA

3. 2cosAcotA

4. None of these

Q.

If $0<x<\pi$ and $\cos x+\sin x=\frac{1}{2}$, then $\tan x$ is equal to

1. $\frac{4–\sqrt{7}}{3}$

2. $-\frac{\left(4–\sqrt{7}\right)}{3}$

3. $\frac{1+\sqrt{7}}{3}$

4. $\frac{1-\sqrt{7}}{3}$

Q. Assertion-Reasons: A: f(x)= sin^-1x+cos^-1x+2, d(f(x))/dx=0 R: d(sinx)/dx=cos x

Q. integrate (x * e ^ log sin x - cos x) dx

Q. 25.cos 6x = 32 cos®x-48cos4 x + 18 cos2x-1

Q.

If sin A = n sin B, then $\frac{n-1}{n+1}$ tan $\frac{A+B}{2}$ =

1. 

2. 

3. 

4. 

Q.

If A + B + C = ${180}^{\circ }$, then sin (B + 2C) + sin (C + 2A) + sin (A + 2B)

1. 4 sin . sin . cos

2. 4 sin . sin . sin

3. 1 + 4 sin . sin . sin

4. 1 + 4 sin . sin . cos