Question

Solve in radians help plz

Answer 1

I think we can use the identity  sin x/2  = sqrt [(1 - cos x) /2]

cos x -  sqrt3 sqrt ( 1 - cos x) /sqrt2 = 1

cos x - sqrt(3/2) sqrt(1 - cos x) = 1
sqrt(3/2)(sqrt(1 - cos x) =  cos x - 1   Squaring both sides:-
1.5 ( 1 - cos x) = cos^2 x - 2 cos x + 1

cos^2 x - 0.5 cos x - 0.5 = 0 

cos x = 1 , -0.5

giving x = 0 , 2pi, 2pi/3,  4pi/3  ( for  0  =< x <= 2pi)

because of thw square roots some of these solutions may be extraneous so we should plug these into the original equations to see if they fit.

The last 2 results dont fit so the answer is  x = 0 , 2pi Answer