If 7 sin^2 x + 3 cos^2 x = 4, then what is the value of tan x

• Quant Trigo

If 7 sin² x + 3 cos² x = 4, 0 < x < 90°, then what is the value of tan x?

1. √2
2. 1
3. √3/2
4. 1/√3

Answer

sin² x + cos² x = 1

4 sin² x + 3(sin² x + cos² x) = 4

4 sin² x = 1

sin² x = 1/4

sin x = 1/2

x = 30°

tan 30° = 1/√3

The correct option is D.