If 7 sin 2 θ + 3 cos 2 θ =4, find the value of tan θ.

Question

Philoid · Accepted Answer

Given : 7 sin² θ + 3 cos² θ =4

⇒ 7 sin² θ + 3(1– sin² θ) = 4 [∵ sin² θ + cos² θ = 1]

⇒ 7 sin² θ + 3 –3 sin² θ = 4

⇒ 4 sin² θ = 4 – 3

⇒ 4 sin² θ = 1

Put the value of in given equation, we get

⇒

Now, we know that tan θ

If 7 sin2 θ + 3 cos2 θ =4, find the value of tan θ.