Solve in radians help plz

Mathematics

1 answer:

PIT_PIT [208]2 years ago

5 0

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

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