verify that that square root of (1-cos(x)/1+cox(x)) = sin(x)/1+cox(x)

Question

trying to verify trig identites

Answer 1

Recall the identity Sin^2(x)+Cos^2(x) = 1

Sin^2(x) = 1-Cos^(x)

Sin^2(x)= (1-Cos(x))(1+Cos(x))

Sin(x) = √(1-Cos(x))√(1+Cos(x))

Sin(x)/√(1+Cos(x)) = √(1-Cos(x)) -----------> (1)

Left hand side =√[(1-Cos(x))/(1+cos(x))]

= √(1-Cos(x))/√(1+Cos(x))

From (1) Substitute the √(1-Cos(x)) value.

= Sin(x)/√(1+Cos(x))/√(1+Cos(x))

= Sin(x)/√(1+Cos(x))√(1+Cos(x))

= Sin(x)/(1+Cos(x))

= Right hand side.