Sum of Trigonometric Ratios in Terms of Their Product

Q.

The maximum value of ${\cos }^2\left(\frac{\mathrm{\pi }}{3}-x\right)-{\cos }^2\left(\frac{\mathrm{\pi }}{3}+x\right)$ is

1. $-\frac{\sqrt{3}}{2}$

2. $\frac{1}{2}$

3. $\frac{\sqrt{3}}{2}$

4. $\frac{3}{2}$

Q.

Express $\sin A$ in terms of $\cot A$.

Q.

Solve for x and y : $12sinx+5cosx=2y^2-8y+21$.

1. 

2. 

3. 

4. 

Q.

In a $△$ ABC, if a cos A = b cos B, show that the triangle is either isosceles or right angled.

Q.

Prove that $4cos{12}^{\circ }cos{48}^{\circ }cos{72}^{\circ }=1-2si{n}^2{18}^{\circ }$.

Q. If $\sin B=\frac{1}{5}\sin (2A+B),$ then $\frac{tan(A+B)}{tanA}$ is equal to

1. 
2. 
3. 
4. 

Q. If $\sin 2\beta$ is the G.M. between $\sin \alpha$ and $\cos \beta$, then $\cos 4\beta$ is equal to

1. 
2. 
3. 
4. 

Q. $\frac{sin7x+6sin5x+17sin3x+12sinx}{sin6x+5sin4x+12sin2x}$
is equal to

1. $sinx$
2. $2sinx$
3. $cosx$
4. $2cosx$

Q. cos4x cos 3x + cos2.x21.sin 4x + sin 3x +sin 2x=cot 3x, r + sin 2x

Q.

Find the value of ($cos{20}^{\circ }-sin{20}^{\circ }$) (1+4$sin{20}^{\circ }cos{20}^{\circ }$)

1. 

2. 

3. 

4. 

Q.

cos 2x =

1. B.

2. A.

3. C.

4. Both B and C

Q. $\cos \theta +\cos ({240}^{\circ }+\theta )+\cos ({240}^{\circ }-\theta )=$

1. 1
2. 
3. 
4. 0

Q.

$1+cos{56}^{\circ }+cos{58}^{\circ }-cos{66}^{\circ }=$

[IIT 1964]

1. 

2. 

3. 

4. 

Q.

If cos (A-B) = $\frac{3}{5}$ and tanAtanB = 2, then

1. cosA cos B =

2. sinA sin B =

3. cos (A+B) =

4. sinAcos B =

Q.

If sinA=sinB and cosA=cosB, then

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

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

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

4. cos (A + B) = 0

Q. $\cos 4\theta -\cos 6\theta$ equals to

1. $2\sin 5\theta \cos \theta$
2. $-2\sin 5\theta \sin \theta$
3. $2\sin \theta \cos 5\theta$
4. $2\sin 5\theta \sin \theta$

Q.

If A+B+C =$\pi$, prove that cos A + cos B - cos C = $\left(4\text{cos}\frac{A}{2}\text{cos}\frac{B}{2}\text{sin}\frac{C}{2}\right)-1$

Q. 22.cot x cot 2x-cot 2x cot 3x-cot 3x cot x = 1

Q. 13. cos-2-cos2 6x = sin 4x sin 8x

Q. 14, sin2 x + 2 sin 4x + sin 6r = 4 cos2 x sin 4x

Q. Consider the polynomial $P\left(x\right)=\left(x-\cos {36}^{\circ }\right)\left(x-\cos {84}^{\circ }\right)\left(x-\cos {156}^{\circ }\right)$ , then coefficient of $x^2$ is

1. 0
2. 1
3. $-\frac{1}{2}$
4. $\frac{\sqrt{5}-1}{2}$

Q. ${\left(\frac{cosA+cosB}{sinA-sinB}\right)}^n+{\left(\frac{sinA+sinB}{cosA-cosB}\right)}^n$ (n even or odd)=

1. 
   
   
2. 
3. 
4. 

Q. If A + B + C = ${180}^{\circ }$ then sin 2A + sin 2B + sin 2C =

1. sin A sin B sin C
2. 4 sin A sin B sin C
3. 3 sin A sin B sin C
4. 2 sin A sin B sin C

Q. 9.sin x + sin 3x + sin 5x = 0

Q. The value of $\underset{x\to 0}{lim}\left[\frac{3\sin 3x}{x}\right]-\left[\frac{2\sin 2x}{x}\right]$ ( where, [.] denotes greatest integer function) is

1. $5$
2. $3$
3. $8$
4. $6$

Q.

$sin{50}^0$ - $sin{70}^0$ + $sin{10}^0$ =

[MNR 1979]

1. 0

2. 1/2

3. 2

4. 1

Q. $\cos \theta +\cos ({240}^{\circ }+\theta )+\cos ({240}^{\circ }-\theta )=$

1. \N
2. 1
3. $\frac{1}{4}$
4. $\frac{3}{4}$

Q. cos E-)c cos E-y -sin E-x sin 2-y =sin(x+y)4 4 4 4

Q. $1+cos{56}^{\circ }+cos{58}^{\circ }-cos{66}^{\circ }=$

1. 
2. 
3. 
4. 

Q. sin x sin 3x20.= 2sinxin x- COS x