Question

If 7sin2x+3cos2x=4 show that tanx=1/√3

Answer 1

7 sin² x + 3 cos ² x = 4

7 sin² x + 3 (1- sin²x) = 4 (since cos² x = 1 - sin² x)

7 sin² x+3 - 3 sin² x = 4

4 sin² x = 1

sin² x = 1/4 

sin x = 1/2

sin x = sin 30 °

x = 30°

LHS 

tan x = tan 30°

= 1/√3  = RHS

Answer 2

7 sin^2 x + 3 cos ^ 2 x = 4
7 sin ^2 x + 3 ( 1 - sin^2 x) = 4 ::::(cos^2 x = 1 - sin^2 x)
7 sin ^ 2 x + 3 - 3 sin ^2 x = 4
 4 sin ^ 2 x = 1 
sin ^2 x = 1/4
sin x = 1/2 
sin x = sin 30 
x = 30 
LHS tan = x = tan = 30
= 1/√3
hence proved LHS =RHS