Question

if 7sin^2theta + cos^2 theta = 4 find the value of tan theta

Answer 1

Here is your answer hope it helps

Answer 2

Note: Your question is incorrect. It should be 3 cos^2 theta.

Now,

Given Equation is 7 sin^2 Ф + cos^2 Ф = 4

⇒ 4 sin^2 Ф + 3 sin^2 Ф + 3 cos^2 Ф = 4

⇒ 4 sin^2 Ф + 3(sin^2 Ф + cos^2 Ф) = 4

⇒ 4 sin^2 Ф + 3 = 4

⇒ 4 sin^2 Ф = 1

⇒ sin^2 Ф = (1/4)

⇒ sin Ф = (1/2).

⇒ sin Ф = sin 30

⇒ Ф = 30

Therefore:

⇒ tan Ф

⇒ tan 30

⇒ (1/√3)

∴ tan theta = (1/√3).

Hope it helps!