show that sin / cosec -1 + cos / 1+sec = sin cos /sin - cos
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LHS ≠ RHS for Sinx/(Cosecx - 1 ) + Cosx/(1 + secx) = Sinx Cosx/(Sinx - Cosx) hence mistake in data
Step-by-step explanation:
Sinx/(Cosecx - 1 ) + Cosx/(1 + secx) = Sinx Cosx/(Sinx - Cosx)
Lets take x = 30°
Sin30° = 1/2
Cosec30° = 2
Cos30° = √3 / 2
Sec30° = 2/√3
LHS = (1/2)/(2 - 1) + (√3 / 2)(1 + 2/√3)
= 1/2 + (3/2)/(√3 + 2)
= (1/2) (1 + 3/(√3 + 2))
= (1/2) ( 1 + 3 (2 - √3))
= (1/2)(7 - 3√3)
= (7 - 3√3)/2
RHS
= (1/2)(√3 /2)/ (1/2 -√3 /2)
= (√3 /2)/ (1 - √3)
= (√3 /2)(√3 + 1)/(-2)
= -(3 + √3)/4
LHS ≠ RHS
Hence mistake in given data
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