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The value of the expression $cosec (75^{0} + θ) - \sec (15^{0} - θ) - \tan (55^{0} + θ) + \cot (35^{0} - θ)$ , is ?

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- 1

0

1

\frac{3}{2}

answer is B.

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Detailed Solution

Given expression is,

cosec (75^{0} + θ) - \sec (15^{0} - θ) - \tan (55^{0} + θ) + \cot (35^{0} - θ)

.
Let the above expression be E.
We know that,

cosec θ = \sec (90^{0} - θ)

and

tanθ = \cot (90^{0} - θ)

.
By using the above trigonometric functions, we get

E = \sec (90^{0} - 75^{0} - θ) - \sec (15^{0} - θ) - \cot (90^{0} - 55^{0} - θ) + \cot (35^{0} - θ)

\Rightarrow E = \sec \sec (15^{0} - θ) - \sec \sec (15^{0} - θ) - \cot \cot (35^{0} - θ) + \cot \cot (35^{0} - θ)

\Rightarrow E = 0

Hence, the correct option is (2).

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