Question

Express the trigonometric ratios cos A and cosec A in terms of tan A.

Answer 1

we know that sin²A + cos²A = 1

dividing the above expression with cos²A we get

tan²A + 1 = sec²A

but we know that secA = 1/cosA

⇒ tan²A + 1 = 1/cos²A

⇒ cos²A = 1/1 + tan²A

⇒ cosA = 1/(Square root of 1 + tan²A)

we know that sin²A + cos²A = 1

dividing the above expression with sin²A we get

1 + cot²A = cosec²A

but we know that cotA = 1/tanA

⇒ 1 + 1/tan²A = cosec²A

⇒ cosecA = Square root of (1 + tan²A)/tanA

Answer 2

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