using trigonometric identities

When the integrand consists of trigonometric function, we use suitable trigonometric identities to simplify the function so that it can be integrated. Few identities are given below for ready reference. (1) (2) (3) (4) (5) (7) (..

1. sin A = cos (90 o - A) 2. 3. tan A x tan (90 o - A) = 1 4. sin 2 A + cos 2 A = 1 5. 1 + tan 2 A = sec 2 A 6. 1 + cot 2 A = cosec 2 A Let us prove the above identities. Let D ABC be a right-angled triangle with B = 90 o . Let BC = a, AC = b and AB = c. (1..

Conditional Trigonometric Identities - In the previous sections many identities have been discussed. They are true for all values of the angles for which trigonometric functions are defined. In this section we prove identities, where a certain relat..

The trigonometric ratio's are: Sine, Cosine, Tangent, Cotangent, Secant, and Cosecan..

1. sin A = cos (90 o - A). 2. sin A / cos a = tan A. 3. tan A x tan (90 o - A) = 1. 4. sin 2 A + cos 2 A = 1. 5. 1 + tan 2 A = sec 2 A. 6. 1 + cot 2 A = cosec 2 A. Where 'A' is the angl..

Summary - sin A = cos (90 o - A) tan A . tan (90 o - A) = 1 sin 2 A + cos 2 A = 1 1 + tan 2 A = sec 2 A 1 + cot 2 A = cosec 2..

Trigonometric tables are used (1). to find the value of a t-ratio when the angle is given. (2). to find the angle when the value of the t-ratio is given. As an angle increases, the sine ratio increases, the cosine ratio decreases and the tangent ratio increase..

Factorisation using Identities - Recall the following identities for finding the products: Observe that the LHS in the identities are all factors and the RHS are their products. Thus, we can write the factors as follow..

Recall the following identities for finding the products: ..