Question

prove this plz


1- cos2x + sin x / sin 2x + cos x = tan x

Answer 1

Work on the left hand side of the identity:

The numerator can be factored as

(cos^2x-sin^2x) = (cos x - sin x)(cos x + sin x)

and the denominator can be rewritten as

cos^2x+sinxcosx = cos x(cos x + sin x)

Rewriting the left side of the given identity,

(cos x - sin x)(cos x + sin x)/(cos x(cos x + sin x))

and since the factor "(cos x + sin x)" appears on the numerator and the denominator, it will cancel out and the above simplifies to

(cos x - sin x)/cos x

The above can be rewritten as

(cos x/cos x) - sin x/cos x

and thus becoming

1 - tan x = right hand side of the given equation.

Hope this helps.