show that q(p square -1)= 2 p , if sin theta + cos theta = p and sec theta + cosec theta = q
Answers
Answered by
1
q(p²-1)
= (secθ+cosecθ){(sinθ+cosθ)²-1}
= (secθ+cosecθ){(sin²θ+cos²θ+2sinθcosθ)-1}
= (secθ+cosecθ){(1+2sinθcosθ)-1}
= (secθ+cosθ)(2sinθcosθ)
= 2(secθ+cosecθ)(sinθcosθ)
= 2(secθsinθcosθ+cosecθsinθcosθ)
= 2(sinθ+cosθ)
= 2p
Similar questions