If √3 tan θ = 3 sin θ, prove that (sin2 θ – cos2 θ) = 1/3.

Given: √3 tanθ = 3 sinθ⇒ ⇒ ⇒ ⇒ Also, we know, ⇒ ⇒ Now, we need to prove that:sin2θ – cos2θ = 1/3⇒ L.H.S = ⇒ L.H.S = ⇒ L.H.S = 1/3

Q7 of 186 Page 359

If √3 tan θ = 3 sin θ, prove that (sin² θ – cos² θ) = 1/3.

Given: √3 tanθ = 3 sinθ

⇒

Also, we know,

⇒

Now, we need to prove that:

sin²θ – cos²θ = 1/3

⇒ L.H.S =

⇒ L.H.S = 1/3

If cot A = 4/5, prove that

If 2x = sec A and 2/x = tan A, prove that .

Prove that .

If 2 sin 2θ = √3, prove that θ = 30°.