Question

prove( 1+cos 2x)/sin 2x = 1

Answer 1

hey there,

Answer:

See the proof in the explanation.

Explanation:

sin2x1−cosx

Multiply the numerator and denominator both by the conjugate of the denominator. This is a "fancy 1" that does not affect the value of the expression.

sin2x1−cosx⋅1+cosx1+cosx

This sets up a Difference of Squares in the denominator. Resist the urge to distribute in the numerator.

(sin2x)(1+cosx)(1)2−(cosx)2=(sin2x)(1+cosx)1−cos2x

Use the Pythagorean Identity sin2x+cos2x=1 to replace the 1 in your denominator.

(sin2x)(1+cosx)(sin2x+cos2x)−cos2x

Simplify the denominator.

(sin2x)(1+cosx)(sin2x)

Simplify the fraction.

1+cosx

Hope this helps!