Assertion (A): sec² θ − tan² θ = 1 for all values of θ where the ratios are defined. Reason (R): The identity 1 + tan² θ = sec² θ is derived from sin² θ + cos² θ = 1.

Free previous-year papers & practice for JEE, NEET and CBSE Boards.

Free previous-year papers & practice for JEE, NEET and CBSE Boards.

Identity Relating Secant and Tangent, Pythagorean Trigonometric Identity | PadhAiPro

Question

Assertion-ReasonIdentity Relating Secant and TangentPythagorean Trigonometric Identity

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

Relationship Between Trigonometric Ratios

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.

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