Question

if 3 cos^2 A + 7 sin^2 A = 4, then what is the value of cot A , given that A is the acute angle​

Answer 1

Answer:

√3

Step-by-step explanation:

3cos² A + 7sin² A = 4

Dividing by sin² A on both sides

3cos² A/sin² A + 7sin² A/sin² A = 4/sin² A

3cot² A + 7 = 4cosec² A

3cot² A + 7 = 4( 1 + cot² A)

3cot² A + 7 = 4 + 4cot² A

7 - 4 = 4cot² A - 3cot² A

3 = cot² A

Taking square root on both sides

√3 = cot A

Therefore the value of cot A is √3.