Prove that: (tanθ+secθ–1)/(tanθ–secθ+1) = (1+sinθ)/cosθ

Question

TextIdentity Relating Secant and Tangent

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

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.

Assertion (A) : For an acute angle θ, sec θ = 3 ⇒ tan θ = 2√2 . Reason (R) : sec²θ = 1 − tan²θ for all values of θ.

Find the value of x for which (sin A + cosec A)² + (cos A + sec A)² = x + tan² A + cot² A

Evaluate the following : (3 sin30° – 4 sin³30°)/(2 sin²50° + 2 cos²50°)