Solveeit Logo
Login

Question

Question: Function f(x) = \(\frac{a\sin x + b\cos x}{c\sin x + d\cos x}\) is monotonic decreasing if –...

Function f(x) = asin⁡x+bcos⁡xcsin⁡x+dcos⁡x\frac{a\sin x + b\cos x}{c\sin x + d\cos x} is monotonic decreasing if –

A

ad – bc < 0

B

ad – bc > 0

C

ab – cd < 0

D

ab – cd > 0

Answer

ad – bc < 0

Explanation

Solution

f ¢(x) = ad−bc(csin⁡x+dcos⁡x)2\frac{ad - bc}{(c\sin x + d\cos x)^{2}} (on solving)

f ¢(x) is monotonic decreasing if f ¢(x) < 0

Ž ad – bc < 0