Question

If $\sin \theta +\cos \theta =P$ and $\sec \theta +\csc \theta =q$, show that

Answer 1

$P=sin\theta +cos\theta andq=sec\theta +cosec\theta$

$=(sec\theta +cosec\theta )\left[\right(sin\theta +cos\theta )²-1]$

$=(\frac{1}{cos\theta }+\frac{1}{sin\theta })(sin²\theta +2sin\theta cos\theta +cos²\theta -1)$

$=\frac{(sin\theta +cos\theta )}{sin\theta cos\theta }\left(2sin\theta cos\theta \right)[Since,sin²\theta +cos²\theta =1]$

$=2(sin\theta +cos\theta )$\\ $=2p\left(Proved\right)$