CosecA -2cot2AcosA=?

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CosecA -2cot2AcosA=?

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Answer 1 · 2018-07-07T06:36:12

$csc A - 2 cot 2 A cos A = 2 sin A$ $csc A - 2 cot 2A cos A = 2 sin A$

Explanation:

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I'll assume that's $cot 2 A$ $cot 2A$ not ${cot}^{2} A$ $cot^2 A$

$csc A - 2 cot 2 A cos A$ $csc A - 2 cot 2A cos A$

$= \frac{1}{sin A} - \frac{2 cos 2 A cos A}{sin 2 A}$ $= 1/sin A - {2 \cos 2A \cos A}/{sin 2A}$

$= \frac{1}{sin A} - \frac{2 cos 2 A cos A}{2 sin A cos A}$ $= 1/sin A - {2 \cos 2A \cos A}/{2 sin A cos A}$

$= \frac{1}{sin A} - \frac{cos 2 A}{2 sin A}$ $= 1/{sin A} - { \cos 2A }/{2 sin A }$

$= \frac{1 - cos 2 A}{sin A}$ $= (1 - cos 2A)/{sin A}$

$= \frac{({sin}^{2} A + {cos}^{2} A) - ({cos}^{2} A - {sin}^{2} A)}{sin A}$ $={ (sin ^2 A + cos ^2A) - (cos^2 A - sin ^2 A)}/{sin A}$

$= \frac{2 {sin}^{2} A}{sin A}$ $={ 2sin ^2 A }/{sin A}$

$= 2 sin A$ $= 2sin A$

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CosecA -2cot2AcosA=?

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