Sin2A and Cos2A in Terms of tanA

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

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

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

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

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

1. $\frac{7}{25}$
2. $\frac{24}{25}$
3. $\frac{25}{24}$
4. $\frac{25}{7}$

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

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