Question

Prove each identity:

a) cos (theta) + sin (theta) tan (theta) = 1/cos (theta)

b) tan (theta) = 1-cos2(theta)/sin2(theta)

Answer 1

cos (theta) + sin (theta) tan (theta) = 1/cos (theta)



sin(theta)
cos (theta) + sin (theta) --------- = 1/cos (theta)
cos(theta)



cos^2(theta) sin(theta)
---------- + sin (theta) --------- = 1/cos (theta)
cos(theta) cos(theta)



cos^2(theta) sin^2(theta) 1
---------- + --------- = ---------
cos(theta) cos(theta) cos(theta)



cos^2(theta) +sin^2(theta) =1

Answer 2

Thank you @SolomonZelman , can you help me with b as well?