If sinθ + cosθ = p and secθ + cosecθ = q, show that q(p²-1) = 2p

Dear Student
Put theta in place of A
SinA + CosA = p

SecA + CosecA = q

Now, p² - 1

= (SinA + CosA)² - 1

= (Sin²A + 2SinACosA + Cos²A) - 1

= [ (Sin²A+Cos²A) + 2SinACosA ] - 1

= [ 1 + 2SinACosA ] - 1

= 2SinACosA                [Equation (i)]

So, q(p² - 1)

= (SecA + CosecA) × (2SinACosA)       [from Equation (i)]

= SecA × (2SinACosA) + CosecA × (2SinACosA)

= (1/CosA) × (2SinACosA) + (1/SinA) × (2SinACosA)

= 2SinA + 2CosA

= 2(SinA + CosA)

= 2p

Regards