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Sign of Trigonometric Ratios in Different Quadrants

90∘-θ sin270∘...

Question

$\frac{cot (90 ° - θ) sin (270 ° + θ) cosec (180 ° + θ)}{cos (- θ) sin (90 ° + θ) tan (360 ° - θ)}$ is equal to

A

sec θ cosec θ

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B

- sec θ cosec θ

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C

- cosec θ

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D

sec θ

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Solution

The correct option is B $- sec θ cosec θ$
$\frac{cot (90 ° - θ) sin (270 ° + θ) cosec (180 ° + θ)}{cos (- θ) sin (90 ° + θ) tan (360 ° - θ)}$
$= \frac{tan θ (- cos θ) (- cosec θ)}{(cos θ) (cos θ) (- tan θ)}$
$= - sec θ cosec θ$

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Sign of Trigonometric Ratios in Different Quadrants

Standard XII Mathematics

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