Question

If 3 cot A = 4, check whether
1-tan2A/1+tan2 A =
cos2 A-sin2 A​

Answer 1

Step-by-step explanation:

3 cot A = 4

4 tan A = 3

tan A = 3/4

tan^2A = 9/16

sin^2A = 9/25 cos^2A = 16/25

LHS = (1 - tan^2A)/(1 + tan^2A) = (16 - 9)/(16 + 9) = 7/25

RHS = cos^2A - sin^2A = 16/25 - 9/25 = 7/25

LHS = RHS

Hence if 3 cotA = 4 then (1 - tan^2A)/(1 + tan^2A) = cos^2A - sin^2A