Question

Solve : $(\sin \theta +\cos \theta )(\sec \theta +cosec\theta )=2+\sec \theta cosec\theta$

Answer 1

$(sin\theta +cos\theta )(sec\theta +cosec\theta )$

$\Rightarrow (sin\theta +cos\theta )(\frac{1}{cos\theta }+\frac{1}{sin\theta })$

$\Rightarrow (sin\theta +cos\theta )\left(\frac{sin\theta +cos\theta }{cos\theta sin\theta }\right)$

$\Rightarrow \frac{(sin\theta +cos\theta {)}^2}{cos\theta sin\theta }$

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

$\Rightarrow \frac{1}{cos\theta sin\theta }+2$

$\Rightarrow 2+sec\theta cosec\theta$