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Question

Mathematics Question on Probability

In the following trigonometry expression, find the value of (MN).(1+cos⁡x)(1−sin⁡x)(sin⁡x+cos⁡x−1)2=MsinN⁡x

A

(A) 3

B

(B) 6

C

(C) 4

D

(D) 2

Answer

(C) 4

Explanation

Solution

Explanation:
Given:(1+cos⁡x)(1−sin⁡x)(sin⁡x+cos⁡x−1)2=MsinN⁡xFormula:(sin⁡x+cos⁡x−1)2=2(1−sin⁡x)(1−cos⁡x)According to the question:⇒(1+cos⁡x)(1−sin⁡x)×2(1−sin⁡x)(1−cos⁡x)=MsinN⁡x⇒2(1+cos⁡x)(1−cos⁡x)=MsinNx⇒2(1−cos2⁡x)=MsinN⁡x⇒2sin2⁡x=MsinN⁡xComparing both sides, we have⇒MN=(2×2)=4Hence, the correct option is (C).