Question

If tan theta= 1/root3, prove that 7 sin^2 theta + 3 cos^2 theta = 1

Answer 1

Solution:

• Given : tan∅ = 1/√3
• To prove : 7sin²∅ + 3cos²∅ = 4

We have ;

=> tan∅ = 1/√3

=> tan∅ = tan30°

=> ∅ = 30°

Now,

7sin²∅ + 3cos²∅ = 7sin²30° + 3cos²∅

= 7×(sin30°)²+ 3×(cos30°)²

= 7×(1/2)² + 3×(√3/2)²

= 7×(1/4) + 3×(3/4)

= 7/4 + 9/4

= (7 + 9)/4

= 16/4

= 4

Thus,

7sin²∅ + 3cos²∅ = 4

Hence proved .