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Question

Mathematics Question on Relations and functions

Let f(x)=sinx+cosx−2sinx−cosx,x∈[0.π]−[π4].Thenf(7π12)fn(7π12)f(x)=\frac{sinx+cosx-\sqrt2}{sinx-cosx},x∈[0.\pi]-\left[\frac{\pi}{4}\right]. Then f\left(\frac{7\pi}{12}\right)f^n\left(\frac{7\pi}{12}\right)is equal to

A

−23\frac{-2}{3}

B

−133\frac{-1}{3\sqrt3}

C

233\frac{2}{3\sqrt3}

D

29\frac{2}{9}

Answer

29\frac{2}{9}

Explanation

Solution

The correct option is(D): 29\frac{2}{9}