In , right-angled at , let . The side lengths are and…

MATHEMATICS · Multi-part · CBSE · Mathematics · Introduction to Trigonometry · Introduction to Trigonometry

Problem

\triangle ABC

, right-angled at

B

, let

\angle A=\theta

. The side lengths are

AB=8\,\text{cm}

and

BC=6\,\text{cm}

. (i) Express

\tan\theta

and

\sec\theta

in terms of the given side lengths. (ii) Without using a calculator, verify that

(1+\tan^2\theta)=\sec^2\theta

by substituting the expressions found in part (i). (iii) Hence, find the numerical value of

\sec\theta