Trigonometry Question

Question

y the numerator and denominator of the fraction by the conjugate of the denominator, and then simplify.

1 − cos x /1 + cos x

Answer 1

Trigonometry Question

Multiply the numerator and denominator of the fraction by the conjugate of the denominator, and then simplify.

(1 − cos x)/(1 + cos x) ==>

(1 − cos x)/(1 + cos x)*(1 − cos x) /(1 - cos x) =(1 − cos x)²/(1 - cos² x) = (1 − cos x)²/( sin² x)

(1 − cos x)²/( sin² x) = (1 − 2 cos x + cos²x)/(sin² x) =

1/sin² x − 2 cos x/sin² x + cos²x/sin² x = csc² x - 2 (cot x)(csc x) + cot²x

Answer 2

it doesn't seem useful, but 1 − cos x /1 + cos x = [(1-cosx)²]/sin²x