The value of the expression [cosec(75^{\circ}+\theta)-\sec (15^{\circ}-\theta)-\tan (55^{\circ}+\theta)+\cot (35^{\circ}-\theta)] is

CMAT 2017 Solved Question Paper

Question : 21 of 100

Marks: +1, -0

The value of the expression

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

Solution:

cosec(75^{∘}+θ)-\sec (15^{∘}-θ)

-\tan (55^{∘}+θ)+\cot (35^{∘}-θ)

=cosec(75^{∘}+θ)-\sec (90^{∘}-(75^{∘}+θ))

=-\tan (55^{∘}+θ)+\cot (90-(55^{∘}+θ))

=cosec(75^{∘}+θ)-cosec(75^{∘}+θ)

-\tan (55^{∘}+θ)+\tan (55^{∘}+θ)

=0

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