Question

(1+tan + sec theta)(1+ cot theta - cosec theta )​

Answer 1

Answer:

(1 + tan theta + sec theta)(1 + cot theta - cosec theta)

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

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

=((cos + sin)² - 1² / cos.sin)                 [(a+b)(a-b) = a2-b2]

=(cos² + sin² + 2sin.cos -1 / cos.sin)

=1 + 2sin.cos -1 / cos.sin                             [ sin2 theta = cos2 theta = 1]

=2sin.cos / cos.sin

=2