Question

√3tanø=3sinøprove that sin^2ø-cos^2ø=1/3​

Answer 1

Answer:

✓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

Step-by-step explanation: