Trigonometric Ratios for Sum of Two Angles

Q. A quadratic equation whose roots are $si{n}^2{18}^{\circ },co{s}^2{36}^{\circ }$ are

1. 
2. None
3. 
4. 

Q.

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

[IIT 1967; MNR 1987; MP PET 1989]

1. None of these

2. 

3. 

4. 

Q.

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

1. 

2. 

3. 

4. 

Q.

If $cos(\theta -\alpha )$ = a, $sin(\theta -\beta )$ = b,

then $co{s}^2(\alpha -\beta )$ + 2ab $sin(\alpha -\beta )$ is equal to

1. 

2. 

3. 

4. 

Q.

If $cos3\theta$ = $\alpha cos\theta +\beta co{s}^3\theta$, then $(\alpha ,\beta )$ =

1. (3, 4)

2. (4, 3)

3. (-3, 4)

4. (3, -4)

Q.

If tan x =n tany, $n\in R^{+}$, then maximum value of $se{c}^2(x-y)=$___

1. $\frac{(n+1{)}^2}{2n}$

2. $\frac{(n+1{)}^2}{2}$

3. $\frac{(n+1{)}^2}{4n}$

4. $\frac{(n+1{)}^2}{n}$

Q.

$\frac{1}{tan3A-tanA}$ - $\frac{1}{cot3A-cotA}$ =

1. tanA

2. cot2A

3. cotA

4. tan2A

Q. The value of ${\sum }_{k=1}^{13}\frac{1}{sin(\frac{\pi }{4}+\frac{(k-1)\pi )}{6})sin(\frac{\pi }{4}+\frac{k\pi }{6})}$ is equal to

1. $2(3-\sqrt{3})$
2. $2(\sqrt{3}-1)$
3. $2(2-\sqrt{3})$
4. $3-\sqrt{3}$

Q. $\sqrt{2}+\sqrt{3}+\sqrt{4}+\sqrt{6}$ is equal to

1. 
2. 
3. 
4. 

Q.

$\frac{1}{4}$$[\sqrt{3}cos{23}^{\circ }-sin{23}^{\circ }]$ =

1. None of these

2. cos43⁰

3. cos7⁰

4. cos53⁰