Verify the identity tantheta sintheta costheta sectheta ta

Verify the identity. tan(theta) sin(theta) + cos(theta) = sec(theta) tan(theta) sin(theta) + cos(theta) = (sin (theta)/cos(theta)) middot sin(theta) + cos(theta) = 1 - cos^2 (theta)/cos(theta) + cos^2 (theta)/cos(theta) = 1/cos(theta) = sec(theta)

Solution

tan theta sin theta   + cos theta= sec theta

Starting with the left side

tan theta sin theta + cos theta

(sin theta/cos theta)sin theta   + cos theta

sin²theta/cos theta     +   cos theta

(sin²theta + cos²theta)/cos theta   = 1/cos theta =sec theta