Question

If 6 sin2x - 2 cos2x = 4,then find the value of tan x?
1. √3 
2. √2 
3. 2
4. None of these

Answer 1

Correct Answer - Option 1 : √3 

Concept:

sin2x + cos2x = 1

 

Calculations:

Given,

6 sin2x - 2 cos2x = 4

⇒ 6 sin2x - 2 cos2x = 4

⇒ 6 sin2x - 2 cos2x = 4 (sin2x + cos2x)

⇒ 6 sin2x - 2 cos2x = 4 sin2x + 4 cos2x

⇒ 6 sin2x - 4 sin2x   = 4 cos2x + 2 cos2x

⇒ 2 sin2 x = 6 cos2x

⇒ tan² x = 3

∴ tan x = √3