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No. of solutions of x,where x belongs to [0,2pie] and satisfies the equation, |sin a| +|cos a | = |sin x| where a is any real number. (Plz provide solution with explanation)

No. of solutions of x,where x belongs to [0,2pie] and satisfies the equation,
|sin a| +|cos a | = |sin x| where a is any real number.
(Plz provide solution with explanation)

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1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
9 years ago
Hello student,
Please find the answer to your question below
Given|sin a| +|cos a | = |sin x| where a is any real number
Squaring LHS we get
(|sin a| +|cos a |)2=sin2a+cos2a+|sin 2a| = 1 +|sin 2a|
Since 0 <= |sin2a| <= 1
so, 1<=(|sin a| +|cos a |)2 <= 2
Hence, we get
|sin x| >=1
which is only possible when |sin x| = 1. That happens only for x = \pi/2, 3\pi/2.
Hence, only 2 solutions are possible.

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