Simplify (1 + tan²θ) (1 – sinθ) (1 + sinθ)

Question

TextPythagorean Trigonometric IdentityIdentity Relating Secant and Tangent

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If sec θ − tan θ = m, then the value of sec θ + tan θ is :

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

Pythagorean Trigonometric Identity

If a sec θ + b tan θ = m and b sec θ + a tan θ = n, prove that a² + n² = b² + m²

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.

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.