Trigonometric equations
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Solve the equation by any means. Find the exact solutions when possible and approximate ones otherwise.
45. 2sinx = 1
55. 2 sin²x - 3 sin x = 2
56. cos 2x = cos x
Hint first use an identity
57. sec²x + 3 tan²x = 13
58. sec² = 4 tan x - 2
59. 2 sin²x + sin x - 2 = 0
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This provides several examples of solving trigonometric equations.
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45)2sinx=1
sinx=1/2
as we know that sin 30=1/2=sin pi/6
so substituting for ½ as sin 30 or sin pi/6
therefore sin x =sin 30
x=30=pi/6
55)2sin^2x-3sinx=2
we can write given equation as
2sin^2x-3sinx-2=0
which is quadratic equation in sinx so splitting the middle term
2sin^2x-4sinx+sinx-2=0
taking 2sinx common from first two terms and +1 common from last two terms
2sinx(sinx-2)+1(sinx-2)=0
(2sinx+1)(sinx-2)=0
2sinx+1=0
sinx=-1/2.........(1)
sinx-2=0
also sinx=2.............(2)
from 1 and 2 we have two values of ...
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