Question

Prove that : ${(sin\theta +sec\theta )}^2+{(cos\theta +cosec\theta )}^2={(1+sec\theta cosec\theta )}^2$.

Answer 1

$(\sin \theta +\sec \theta {)}^2+(\cos \theta +cosec\theta {)}^2=(1+cosec\theta .\sec \theta {)}^2$

$={\sin }^2\theta +2\sin \theta .\sec \theta +{\cos }^2\theta +cose{c}^2\theta +2\cos \theta .cosec\theta$

$=1+{\sec }^2\theta +cose{c}^2\theta +2\frac{\sec \theta }{cosec\theta }+\frac{cosec\theta }{\sec \theta }$

$=1+{\sec }^2\theta +cose{c}^2\theta +2cosec\theta .\sec \theta$

$=(1+cosec\theta .\sec \theta {)}^2$