Question

Evaluate
$\tan \theta .\sin \theta +\cos \theta =\sec \theta$

Answer 1

Changing LHS into sine, cosine,

$\Rightarrow$ $\frac{si{n}^2\theta }{cos\theta }+cos\theta$

Taking LCM,

$\Rightarrow$ $\frac{si{n}^2\theta +co{s}^2\theta }{cos\theta }$

$\Rightarrow$ $\frac{1}{cos\theta }$

$\Rightarrow$ $sec\theta$ = RHS

Hence proved.