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)

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 = /2, 3/2.
Hence, only 2 solutions are possible.