Question

Prove that ,y = sinP θ cosq θ is maximum at tan θ = √(p/q).

Answer 1

+ (p cot θ – q tan θ) × 0

= -y {(q + p) + (p + q)} + 0

= -2y (p + q)

= -2 (sin^p θ cos^q θ) (p + q)

= -ve

So, y will be maximum

Hence, y will be of maximum value if