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# If sin theta + cos theta =p and sec thet + cosec theta = q , show that q ( p square - 1) = 2p

20 Points
4 years ago
q(p square -1)=sec theta +cosec theta ( (sin theta +cos theta )square -1)=1/cos theta +1/sin theta (2sin theta cos theta )=(sin theta +cos theta )2=2p

Jayanth Miriyala
26 Points
4 years ago
q(p^2-1)= sec theta + cosec theta((sin theta +cos theta)^2 -1)
sec theta + cosec theta( sin^2 theta + cos^2 theta + 2 sin theta cos theta)-1)             (sin^2 theta + cos^2 theta=1)
1/cos theta +1 /sin theta(2 sin theta cos theta)            take LCM
sin theta+ costheta/sin theta cos theta(2 sin theta cos theta)

2(sin theta+ cos theta) = 2p