If sin + cos = p and sec + cosec = q, then prove that
q ( p2 – 1 ) = 2p
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Step-by-step explanation:
q ( p2 – 1 ) = 2p
LHS= q ( p2 – 1 )
= sec+cosec[(sin+cos)2-1]
= sec+cosec[sin2+cos2+2sin.cos-1]
=(1/cos+ 1/sin) [1+2sin.cos-1]
[Identity: sin2=cos2=1]
=(sin+cos/sin.cos)[2sin.cos]
=sin+cos/sin.cos*2sin.cos
=2(sin+cos)
=2p
There fore, 2p=RHS
Hence, LHS=RHS
q ( p2 – 1 ) = 2p proved.
I hope it's help u..!
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