Question

In the following trigonometry expression, find the value of (MN).$\frac{(1+\cos x)}{(1-\sin x)}(\sin x+\cos x-1{)}^2=M{\sin }^{N}x$

• (A) 3
• (B) 6
• (C) 4
• (D) 2

Answer 1

The Correct Option is C

Explanation:
Given:$\frac{(1+\cos x)}{(1-\sin x)}(\sin x+\cos x-1{)}^2=M{\sin }^{N}x$Formula:$(\sin x+\cos x-1{)}^2=2(1-\sin x)(1-\cos x)$According to the question:$\Rightarrow \frac{(1+\cos x)}{(1-\sin x)}\times 2(1-\sin x)(1-\cos x)=M{\sin }^{N}x$$\Rightarrow 2(1+\cos x)(1-\cos x)={\mathrm{Msin}}^{N}x$$\Rightarrow 2(1-{\cos }^{2}x)=M{\sin }^{N}x$$\Rightarrow 2{\sin }^{2}x=M{\sin }^{N}x$Comparing both sides, we have$\Rightarrow \mathrm{MN}=(2\times 2)=4$Hence, the correct option is (C).