Complete the identity sin xcos x 2 1 2 sin x cos x sec2

Complete the identity ( sin x+cos x 2 = ? 1 +2 sin x cos x - sec2 x B) 1 - sin x C) D) o

Solution

( sin x + cos x )^2 / ( 1 + 2 sin x cos x )

simplifying top part

( sin^2 x + 2 sin x cos x + cos^2 x ) / ( 1 + 2 sin x cos x )

from the pythagorean identity

sin^2 x + cos^2 x = 1

so top part becomes

(1 + 2 sin x cos x )

now we have

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

which is equal to 1

so , option c is correct