Question

4cos^2A-3=0
find
angle a
cos 3a
tan^2 A + cos^2 A​

Answer 1

Answer:

(a) 0

(b) 13/12

Step-by-step explanation:

Given,

4 cos²A - 3 = 0

=> 4 cos²A = 3

=> cos²A = 3/4

=> cosA = √3/2

=> cos 30° = √3/2

So, angle = 30°

Now,

(a) cos3A = 4cos³A - 3cosA

= 4 (√3/2)³ - 3 (√3/2)

= 4x3√3/8 - 3√3/2

= 3√3/2 - 3√3/2

= 0

(b) tan²A + cos²A = (1/√3)² + (√3/2)² ; [A = 30°]

= 1/3 + 3/4

= 13/12