Question

minus tan theta cos 90 - theta + sec theta cosec 90 minus theta

Answer 1

cot(90-theta) = tan theta

cosec(90-theta) = sec theta

tan(90-theta) = cot theta

Now, According to question,

tan theta / tan theta + sec theta.sin theta / cot theta

1 + sec theta.sin^2 theta / cos theta (Since, cot theta = cos theta / sin theta)

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

1 + tan^2 theta (1 + tan^2 theta = sec^2 theta)

sec^2 theta