Question

Primary Trigonometric Identities

Answer 1

(1) An equation is called an identity if it is true for all values of the variable(s) involved.

(2) An equation involving trigonometric ratios of an angle is called a trigonometric identity if it is true for all values of the angle.

ln L,ABC, right-angled atB,By Pythagoras Theorem.

AB² + BC² = AC² 

Dividing each term ol (l)by AC², 

This is true for all values of A such that 0° < A < 90°. So, this is a trigonometric identity. now divide eqn.(1) by AB².

Isthis equationtrueforA:0°? Yes,itis. What aboutA = 90°? Well, tanA and secA are not defined for A=90°.

So, eqn. (iii) is true for all values of A such that 0" < A < 90

dividing eqn. (i) by BC².

Note that cosec A and cot A are not defined lor all A = 0°. Therefore eqn. (iv) is true for all value of A such that 0 < A ≤ 90°

Using these identities, we can express each trigonometric ratio in terms of other trigonometric rattos, i.e., i any one of the ratios is known , we can also determine the values of other trigonometric ratios.