Question

Prove that:
cos θ + tan θ sin θ = sec θ

I know the half solution (check the attached image for half solution) and I do not have the other part of solution so having trouble in proving it.​

Answer 1

Answer:

=$\cos \: a \: + \frac{ \sin {}^{2} \: a }{cos \: \: a} \\ = \frac{ {cos }^{2}a + sin {}^{2}a }{cos \: a } \\= \frac{1}{cos \: a} \\= sec \: a$