Verify the identity 1 sin2t 6 cos2t2 49 sin2t cos2t 49 c

Verify the identity. (1 - sin^2(t) + 6 cos^2(t))^2 + 49 sin^2(t) cos^2(t) = 49 cos^2(t) (1 - sin^2(t) + 6 cos^2(t))^2 + 49 sin^2(t) cos^2(t) = (7 cos^2(t))^2 + = 49 cos^2(t)(cos^2(t) +

Solution

( 1 - sin^2t + 6cos^2t)^2 + 49sin^2tcos^2t = 49cos^t

LHS ( sin^2t +cos^2t - sin^2t +6cos^2t)^2 +49sin^2tcos^2t

(7cos^2t)^2 +49sin^2tcos^2t

49cos^4t + 49sin^2tcos^2t

49cos^2t(sin^2t +cos^2t) = 49cos^2t = RHS