Question

If 7 sin^2 theta 3 cos^2 theta = 4, prove that, tan theta= 1/root3

Answer 1

7sin²Ф + 3cos²Ф = 4
⇒ 4sin²Ф + 3sin²Ф + 3cos²Ф = 4
⇒ 4sin²Ф + 3(sin²Ф + cos²Ф) = 4
⇒ 4sin²Ф + 3(1) = 4
⇒ 4sin²Ф = 4 - 3
⇒ 4sin²Ф = 1
⇒ sin²Ф = 1/4
⇒ sinФ = √(1/4)
⇒ sinФ = 1/2
⇒ Ф = 30°

tanФ = tan30° = 1/√3

Answer 2

7 sin² A  + 3 Cos² A = 4
7 sin² A + 3 (1 - sin²A) = 4
4 sin² A = 1
Sin² A = 1/4
Cos² A  = 1 - 1/4 = 3/4

Tan² A = (1/4) / (3/4) = 1/3

Tan A = + 1/√3  or  - 1/√3

there are two answers for the given exercise.