Sin x-cosx/sinx+cosz + sinx+cos x/ sin x -cos x = 2/ 2sin2x -1
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Step-by-step explanation:
[sinx - cosx/sinx + cosx] +[ sinx+cosx/sinx-cosx] = 2/2sin²x -1
//take LCM of denominators
(sinx-cosx)² + (sinx+cosx)² / (sinx+cosx)(sinx-cosx)
//remember (a+b)² + (a-b)² = 2(a²+b²)
=> 2(sin²x + cos²x)/ (sin²x - cos²x)
=> 2/ (sin²x - cos²x)
=> 2/(sin²x - (1-sin²x))
=> 2/(sin²x - 1 + sin²x)
=> 2/ 2sin²x - 1
= R.H.S
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