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Question 3
The value of the expression
cosec(75+θ)sec(15θ)tan(55+θ)+cot(35θ) is

(A) -1
(B) 0
(C) 1
(D) 32

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Solution

The answer is (B).
Thinking Process
We see that the given trigonometric angle of the ratio are the reciprocal in the sense of sign. Then, use the following formulae

i) cosec(90θ)=secθ

ii) cot(90θ)=tanθ

Given, expression =cosec(75+θ)sec(15θ)tan(55+θ)+cot(35θ)

=cosec90(15θ)sec(15theta)tan(55+θ)+cot{90(55+θ)}

=sec(15θ)sec(15θ)tan(55+θ)+tan(55+θ)cosec(90θ)=secθ and cot(90θ)

= 0

Hence, the required value of the given expression is 0.

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