Tan (65-θ)-cot (25-θ)-sec (55-θ)+operatorname{cosec}(35-θ)=ldots ldots ldots ldots . . (where, 0

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8. Introduction to Trigonometry

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$\tan (65-\theta)-\cot (25-\theta)-\sec (55-\theta)+\operatorname{cosec}(35-\theta)=\ldots \ldots \ldots \ldots . .$ (where, $0 < \theta < 25)$

A

$3$

B

$1$

C

$2$

D

$0$

Solution

$\tan (65+\theta)=\cot [90-(65+\theta)]=\cot (25-\theta)$

and $\operatorname{cosec}(35+\theta)=\sec [90-(35+\theta)]=\sec (55-\theta)$

Now, $\tan (65+\theta)-\cot (25-\theta)-\sec (55-\theta)+\operatorname{cosec}(35+\theta)$

$=\cot (25-\theta)-\cot (25-\theta)-\sec (55-\theta)+\sec (55-\theta)$

$=0$

Standard 10

Mathematics

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