Question

Simplify the expression ?

Answer 1

Answer:

The answer is cscx(cscx - 1) ⇒ the second answer

Step-by-step explanation:

∵ csc²x = cot²x + 1

∴ $\frac{cot^{2}x+1-1 }{1+sinx}=\frac{cot^{2}x }{1+sinx}$

Multiply the fraction by its conjugate 1 - sinx (up and down)

∴ $\frac{cot^{2}x }{1+sinx}*\frac{1-sinx}{1-sinx}=\frac{cot^{2}x(1-sinx) }{1-sin^{2}x}$

∵ 1 - sin²x = cox²x

∴ $\frac{cot^{2}x(1-sinx) }{cos^{2}x }$

∵ cot²x = cos²x/sin²x

∴ $\frac{1-sinx}{sin^{x}}=\frac{1}{sin^{2}x}-\frac{sinx}{sin^{2}x}=csc^{2}x-cscx$

Take cscx as a common factor

∴ cscx(cscx - 1)