Question

if root 3 tan theta equal to 2 Sin Theta then find the value of sin square theta minus cos square theta​

Answer 1

Step-by-step explanation:

the image has the answer

Answer 2

Solution :-

⇒ √3tan θ = 2sinθ

⇒ tanθ * ( 1/sinθ) = 2/√3

⇒ sinθ/cosθ * ( 1/sinθ ) = 2/√3

[ Because tanθ = sinθ/cosθ ]

⇒ 1/cosθ = 2/√3

⇒ cosθ = √3/2

⇒ cosθ = cos30°

[ Because cos30° = √3/2 ]

Comparing on both sides

⇒ θ = 30°

Now, sin²θ - cos²θ

= sin²30° - cos²30°

[ Because θ = 30° ]

= ( 1/2 )² - ( √3/2 )²

[ Because cos30° = √3/2 and sin30° = 1/2 ]

= 1/4 - 3/4

= - 2/4

= - 1/2

Therefore the value of sin²θ - cos²θ is - 1/2.