Prove the following identities, where the angles involved are acute angles for which the expressions are defined.

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Question

CASE_STUDIESPythagorean Trigonometric Identity10 sub-questions

Prove that : tan θ/(1 − cot θ) + cot θ/(1 − tan θ) = 1 + sec θ cosec θ

Use the identity : sin²A + cos²A = 1 to prove that tan²A + 1 = sec²A. Hence, find the value of tan A, when sec A = 5/3, where A is an acute angle.

Pythagorean Trigonometric Identity

Identity Relating Secant and Tangent

Prove that : (cos θ – 2 cos³θ)/(sin θ – 2 sin³θ) + cot θ = 0.

Given that sin θ + cos θ = x, prove that sin⁴θ + cos⁴θ = (2 – (x² – 1)²)/2.

If sin A = y, then express cos A and tan A in terms of y.

Prove the following trigonometric identity : (1 + cosec A)/cosec A = cos² A/(1 − sin A)