Sin2A and Cos2A in Terms of tanA

Q.

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

1. |a|

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

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

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

Q.

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

1. $\frac{1}{3}$

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

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

4. $\frac{1}{9}$

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$\theta$ = 1 $\frac{1}{4}$, then tan $\frac{\theta }{2}$ =

1. 

2. 

3. 

4. 

Q.

Prove that $tan{70}^{\circ }=tan{20}^{\circ }+2tan{50}^{\circ }.$
Or

Prove that $1+cos2x+cos4x+cos6x=4cosxcos2xcos3x$

Q. In $\Delta ABC,$ if $a=(b-c)\sec \theta ,$ then $\frac{2\sqrt{bc}}{|b-c|}\sin \frac{A}{2}=$

1. $\cot \theta$
2. $\cos \theta$
3. $\sec \theta$
4. $\tan \theta$

Q. Find for , x in quadrant II

Q. 7 . sin2x + cosx = 0

Q. If ${\sin }^{2}x+\sin x-1=0$, then the value of ${\cos }^{12}x+3{\cos }^{10}x+3{\cos }^{8}x+{\cos }^{6}x$ is

1. $1$
2. $8$
3. $-1$
4. $-8$

Q. 2, x lies in second quadrant.2.sin x =

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. $y=z$
2. $y+z=a+c$
3. $y-z=a+c$
4. $y-z=(a-c{)}^2+4b^2$

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. $\frac{7}{\sqrt{2}}$

2. $\frac{7}{5\sqrt{2}}$

3. $\frac{7}{\sqrt{5}}$

4. $\frac{7}{2\sqrt{5}}$