Question

If √3 tan theta = 3 sin theta then find value of sin²theta -cos²theta

Answer 1

✓3 tanθ = 3 sinθ
✓3 sinθ/cosθ = 3 sinθ

✓3 will cut 3 and sin theta wil be cancelled

1/cosθ = ✓3
cosθ = 1/✓3

Squaring on both sides :

cos²θ = 1/3. ...... equation (1)

1-sin²θ = 1/3
sin²θ = 1 - 1/3
sin²θ = 2/3. ....... equation (2)

Now,
Subtracting equation (1) from (2)...

sin²θ - cos²θ = (2/3)² - (1/3)²
= 4/9 - 1/9
= 3/9
= 1/3 ..... Answer

Hope this helps you....:)

Answer 2

✓3 tanθ = 3 sinθ

✓3 sinθ/cosθ = 3 sinθ

✓3 will cut 3 and sin theta wil be cancelled

1/cosθ = ✓3

cosθ = 1/✓3

Squaring on both sides :

cos²θ = 1/3. ...... equation (1)

1-sin²θ = 1/3

sin²θ = 1 - 1/3

sin²θ = 2/3. ....... equation (2)

Now,

Subtracting equation (1) from (2)...

2/3 - 1/3 = 1/3