Question

show that q(p square -1)= 2 p , if sin theta + cos theta = p and sec theta + cosec theta = q​

Answer 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