Sin2a and Cos2a in Terms of Tana

Q.

Prove that:

${\text{sin}}^2\frac{\pi }{6}+{\text{cos}}^2\frac{\pi }{3}-{\text{tan}}^2\frac{\pi }{4}$ =- $\frac{1}{2}$

Q. If $P_n={\cos }^{n}x+{\sin }^{n}x,$ then $2P_6-3P_4+1=$

1. 0
2. 2
3. 3
4. 1

Q.

Find the value of tan $\frac{\pi }{8}$.

Q.

If sinx + cosx = $\frac{1}{5}$ then cot x is equal to ________.

1. 

2. 

3. 

4. 

Q. If $\underset{x\to 0}{lim}\frac{\left(\right(a-n)nx-\tan x)\sin nx}{x^2}=0$ where n is nonzero real number, then a is equal to

1. 
2. 
3. 
4. 

Q.

In a $△ABC,a=5,b=4andtan\frac{C}{2}=\sqrt{\frac{7}{8}}$. The side c is

1. 6

2. 3

3. 2

4. None of these

Q.

If m = $\frac{sinA}{sinB}$ find $\frac{m+1}{m-1}$

1. tancot

2. 

3. tancot

4. 

Q.

$\sqrt{3}+i=(a+ib)(c+id),then{\tan }^{-1}\frac{b}{a}+{\tan }^{-1}\frac{d}{c}$

has the value

1. 

2. 

3. 

4. 

Q. If $cosec\theta =\frac{p+q}{(p-q)},thencot(\frac{\pi }{4}+\frac{\theta }{2})$=

1. 
2. 
3. 
4. 
   

Q.

Prove $x=n\pi +(-1{)}^n.\frac{\pi }{2}$ or $x=(n\pi +\frac{3\pi }{4})$, where m, $n\in I$

Q.

If tan $\frac{\varphi }{2}$ = 2, find the value of $\frac{5}{4}sin\varphi$.

__

Q. If $\frac{\sin x}{a}=\frac{\cos x}{b}=\frac{\tan x}{c}=k$, then $bc+\frac{1}{ck}+\frac{ak}{1+bk}$ is equal to

1. 
2. 
3. 
4. 

Q.

If $\frac{cosx}{a}=\frac{sinx}{b}$ then $|acos2x+bsin2x|=$

1. $|a\sqrt{ab}|$

2. $\frac{b^2}{|a|}$

3. $\frac{a^2}{|b|}$

4. |a|

Q.

If cos 2 B = $\frac{cos(A+C)}{cos(A-C)}$, then tan A, tan B, tan C are in

1. A.P.

2. G.P.

3. H.P.

4. None of these

Q.

$\text{The value of}\underset{x\to 0}{lim}\frac{1}{x}si{n}^{-1}\left(\frac{2x}{1+x^2}\right)\text{is}$

1. 2

2. 0

3. Does not exist

4. ∞

Q. If $tanx=\frac{2b}{a-c}(a\ne c),y=aco{s}^{2}x+2bsinxcosx+csi{n}^{2}xandz=asi{n}^{2}x-2bsinxcosx+co{s}^{2}x,$ then

1. 
2. 
3. 
4. 

Q.

In any $\Delta ABC,$ prove that

$\frac{(B-C)}{(B+C)}=\frac{tan\frac{1}{2}(B-C)}{tan\frac{1}{2}(B+C)}$

Q.

Prove that sin${}^2\frac{\pi }{6}$ + cos ${}^2\frac{\pi }{3}$ - tan ${}^2\frac{\pi }{4}$ = -$\frac{1}{2}$.

Q.

If $\frac{cosx}{a}=\frac{sinx}{b}$ then $|acos2x+bsin2x|=$

1. $|a\sqrt{ab}|$

2. |a|

3. $\frac{b^2}{|a|}$

4. $\frac{a^2}{|b|}$

Q. If cos x +cosy = $\frac{1}{3}$, sin x + sin y = $\frac{1}{4}$ then sin (x + y) =

1. 
2. 
3. 
4. 

Q. If $\frac{sin\alpha }{a}=\frac{cos\alpha }{b},thenasin2\alpha +bcos2\alpha$ =

1. a
2. b
3. a+b
4. ab

Q. If $\tan A=\frac{x=\sin B}{1-x\cos B}$ and $\tan B=\frac{y\sin A}{1-y\cos A}$ then $\frac{\sin A}{\sin B}=$

1. 
2. 
3. 
4. 

Q.

If a tan $\theta$ = b, then a cos 2$\theta$ + b sin 2$\theta$ =

1. b

2. -a

3. a

4. -b

Q.

If cos $\theta$ = $\frac{3}{5}$ and cos $\varphi$ = $\frac{4}{5}$, where $\theta$ and $\varphi$ are

positive acute angles, then cos $\frac{\theta -\varphi }{2}$ =

1. 

2. 

3. 

4. 

Q.

If sec$\theta$ = $\frac{5}{4}$, then tan $\frac{\theta }{2}$ =

1. 

2. 

3. 

4.