Q1 of 46 Page 291

Evaluate the following :

A. (1 + tanθ + secθ)(1 + cotθ – cosecθ)

We have



⇒


⇒


⇒ [∵, (a + b)(a – b) = a2 – b2]


⇒ [∵, (a + b)2 = a2 + b2 + 2ab]


⇒ [∵, sin2 θ + cos2 θ = 1]


⇒


Thus, (1 + tan θ + sec θ)(1 + cot θ – cosec θ) = 2.


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