Question

sin A =2 by 3 find cos A ,tan A ,sec A ,cosec A ,cot A

Answer 1

Answer:

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Answer 2

${\huge{\star{\red{\bold{\boxed{\boxed{Answer}}}}}}}{\huge{\star}}$

${\red{cosA\: =\: \sqrt{5}/3\\ tanA\: =\: 2/\sqrt{5}\\ secA\: =\: 3/\sqrt{5}\\cosecA\: =\: 3/2\\ cotA\: =\: \sqrt{5}/2 }}$

⭐${\blue{\huge{Explanation}}}$⭐

By formula, sin²A + cos²A = 1

(2/3)² + cos²A = 1

cos²A = 1 - 4/9

cos²A = 5/9

cosA = √5/3

By relation between trigonometric ratios, tanA = sinA/cosA

tanA = 2/3÷√5/3

tanA = 2/√5

By relation between trigonometric ratios, secA = 1/cosA

secA = 1÷√5/3

secA = 3/√5

By relation between trigonometric ratios, cosecA = 1/sinA

cosecA = 1÷2/3

cosecA = 3/2

By relation between trigonometric ratios, cotA = 1/tanA

cotA = 1÷2/√5

cotA = √5/2

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