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Mathematics
Fisher Villa
25 December, 04:40
How do I solve?
5 sin 4x = - 10 sin 2x
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Soren Smith
25 December, 06:01
0
Solve 5sin 4x = - 10sin 2x
Ans: 0, pi/2, pi
Explanation:
sin 4x = 2sin 2x. cos 2x
10sin 2x. cos 2x + 10sin 2x = 0
10sin 2x (cos 2x + 1) = 0
a. sin 2x = 0 - - >
2x = 0 - - > x = 0
2x = pi - - > x = pi/2
2x = 2pi x = pi
b. cos 2x = - 1 - - > 2x = pi - - > x = pi/2
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Samir Vaughn
25 December, 06:21
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Move 5cos (x) 5cos (x) to the left side of the equation by subtracting it from both sides. 5sin (2x) - 5cos (x) = 0 5sin (2x) - 5cos (x) = 0 Simplify each term. Apply the sine double-angle identity. 5 (2sin (x) cos (x)) - 5cos (x) = 0 5 (2sin (x) cos (x)) - 5cos (x) = 0 Multiply 22 by 55 to get 1010. 10 (sin (x) cos (x)) - 5cos (x) = 0 10 (sin (x) cos (x)) - 5cos (x) = 0 Remove parentheses around sin (x) cos (x) sin (x) cos (x). 10sin (x) cos (x) - 5cos (x) = 0 10sin (x) cos (x) - 5cos (x) = 0 Factor 5cos (x) 5cos (x) out of 10sin (x) cos (x) - 5cos (x) 10sin (x) cos (x) - 5cos (x).
Factor 5cos (x) 5cos (x) out of 10sin (x) cos (x) 10sin (x) cos (x). 5cos (x) (2sin (x)) - 5cos (x) = 0 5cos (x) (2sin (x)) - 5cos (x) = 0 Factor 5cos (x) 5cos (x) out of - 5cos (x) - 5cos (x). 5cos (x) (2sin (x)) + 5cos (x) (-1) = 0 5cos (x) (2sin (x)) + 5cos (x) (-1) = 0 Factor 5cos (x) 5cos (x) out of 5cos (x) (2sin (x)) + 5cos (x) ⋅-1 5cos (x) (2sin (x)) + 5cos (x) ⋅-1. 5cos (x) (2sin (x) - 1) = 0
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