1/2 sec x-1=0, 4 tan ^2 x-1=tan^2x, 4sin^2x-3=0 , 2 cos 2x = square root of 2

Question

solve the equations for 0 ≤ x < 2pie

Answer 1

Equation No 1- 1/2 sec x -1 = 0 ; (1/2)*(1/cos x) = 1 ; 2 cos x = 1 ; cos x = 1/2 ; x = 1.074 rads. 

 

Equation No 2- 4 tan ^2 x -1 = tan^2 x; 3 tan^2 x = 1 ; tan^2 x = 1/3; tan x = 1/√3 = √3/3;

x = 0.537 rad 

 

Equation No 3- 2cos 2x =√2 ; cos 2x= √2/2 ; 2x = cos‾¹ (√2/2) =0.7853 rad; x = 0.7853/2 = 0.3927 rad.