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Trigonometric equations

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

Solution Preview

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 ...

Solution Summary

This provides several examples of solving trigonometric equations.

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