Question

Prove:
$\sec \theta (1-\sin \theta )(\sec \theta +\tan \theta )=1$

Answer 1

Convert given equation into $sine,cosine$

We get,

$\frac{1}{\cos \theta }(1+sin\theta )\left(\frac{1-sin\theta }{cos\theta }\right)=1$

Solving LHS,

=> $\frac{1-si{n}^2\theta }{co{s}^2\theta }$

=> $\frac{co{s}^2\theta }{co{s}^2\theta }$

=> $1=$ RHS,

Hence proved