Consider ΔACB, right-angled at C, in which AB = 29 units, BC = 21 units and ∠ABC = θ. Determine the values of (i) cos²θ + sin²θ, (ii) cos²θ – sin²θ

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

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

Trigonometric Ratios of an Acute Angle, Pythagorean Trigonometric Identity | PadhAiPro

Question

TextTrigonometric Ratios of an Acute AnglePythagorean Trigonometric Identity

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

In a right triangle ABC, right-angled at A, if sin B = 1/4, then the value of sec B is

Trigonometric Ratios of an Acute Angle

Reciprocal and Quotient Relations of Trigonometric Ratios

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.

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