Trigonometry — MATHS STD 10 — Question

2
Explanation;
Hint:
(1 + tan θ + sec θ) (1 + cot θ – cosec θ)
= `(1 + sin theta/costheta + 1/cos theta) (1 + cos theta/sin theta - 1/sin theta)`
= `((cos theta + sin theta + 1)/cos theta) ((sin theta + cos theta - 1)/sin theta)`
= `((sin theta + cos theta)^2 - 1)/(sin theta cos theta)`
= `(cos^2theta + sin^2theta + 2sin theta cos theta - 1)/(sin theta cos theta)`
= `(1 + 2sin theta cos theta - 1)/(sin theta cos theta)`
= `(2sin theta cos theta)/(sin theta cos theta)`
= 2