CBSE Class 10 Maths (Standard) 2025 · Paper 30/6/1 · Question 22(b)

Introduction to Trigonometry 2 marks Medium

Use the identity

sin^{2} A + cos^{2} A = 1

to prove that

tan^{2} A + 1 = sec^{2} A

. Hence, find the value of

tan A

, when

sec A = \frac{5}{3}

, where

A

is an acute angle.

Answer

Dividing

sin^{2} A + cos^{2} A = 1

cos^{2} A

proves

tan^{2} A + 1 = sec^{2} A

, and with

sec A = \frac{5}{3}

it gives

tan A = \frac{4}{3}

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