. State whether the following are true or false. Justify your answer. (i) sin (A + B) = sin A + sin B.
(ii) The value of sin increases as increases. (iii) The value of cos increases as increases. (iv) sin = cos for all values of . (v) cot A is not defined for A = °.
. Trigonometric Identities You may recall that an equation is called an identity when it is true for all values of the variables involved. Similarly, an equation involving trigonometric ratios of an angle is called a trigonometric identity, if it is true for all values of the angle(s) involved. In this section, we will prove one trigonometric identity, and use it further to prove other useful trigonometric identities.
In ABC, right-angled at B (see Fig. . ), we have: AB + BC = AC ( ) Dividing each term of ( ) by AC ,