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Question: If f(x) = \(\frac{a\sin x + b\cos x}{c\sin x + d\cos x}\)is decreasing for all x, then-...

If f(x) = asin⁡x+bcos⁡xcsin⁡x+dcos⁡x\frac{a\sin x + b\cos x}{c\sin x + d\cos x}is decreasing for all x, then-

A

ad – bc > 0

B

ad – bc < 0

C

ab – cd > 0

D

ab –cd < 0

Answer

ad – bc < 0

Explanation

Solution

Since f(x)=asin⁡x+bcos⁡xcsin⁡x+dcos⁡x\frac{a\sin x + b\cos x}{c\sin x + d\cos x}is decreasing for all x.

\ f ¢ (x) x < 0 for all x

̃ ad−bc(csin⁡x+dcos⁡x)2\frac{ad - bc}{(c\sin x + d\cos x)^{2}}< 0 for all x.

̃ ad – bc < 0