Question

Simplify:${\exp }^{\left\{{\sin }^{2}x+{\sin }^{4}x+{\sin }^{6}x+......\right\}}$

Answer 1

We have,

${\exp }^{\left\{{\sin }^{2}x+{\sin }^{4}x+{\sin }^{6}x+......\right\}}$

Since,

$a={\sin }^{2}x,r={\sin }^{2}x$

Therefore,

$\Rightarrow ex{p}^{\left(\frac{{\sin }^{2}x}{1-{\sin }^{2}x}\right)}$

$\Rightarrow ex{p}^{\left(\frac{{\sin }^{2}x}{{\cos }^{2}x}\right)}$

$\Rightarrow ex{p}^{\left({\tan }^{2}x\right)}$

Hence, this is the answer.