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Trigonometric Ratios of Compound Angles

The value of ...

Question

The value of $cot 10 ° (cot 40 ° - cot 50 °)$ is equal to

A

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B

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C

2

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D

3

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Solution

The correct option is C $2$
$cot 10 ° (cot 40 ° - cot 50 °) = cot (50 ° - 40 °) (cot 40 ° - cot 50 °) = (\frac{cot 50 ° cot 40 ° + 1}{cot 40 ° - cot 50 °}) \cdot (cot 40 ° - cot 50 °) = cot 50 ° \cdot tan (90 ° - 40 °) + 1 = 2$

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Trigonometric Ratios of Compound Angles

Standard XII Mathematics

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