3 years ago

Solve: sin5x - cos2x + sin x = 0.

Mathematics

1 answer:

mote1985 [20]3 years ago

8 0

Answer:

x = 10 , 45 degrees.

Step-by-step explanation:

This seems a tricky one .

I guess we can use sin A + sin B = 2 sin (A+B)/2 cos (A - B) / 2

so sin 5x + sin x = 2 sin 3x cos 2x so our equation becomes

2 sin 3x cos 2x - cos 2x = 0

cos 2x ( 2 sin 3x - 1) = 0

so 2 sin 3x = 1

sin 3x = 1/2

giving 3x = 30 degrees and x = 10 degrees

or cos 2x = 0

so 2x = 90

giving x = 45 degrees.

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$f(x)=e^{-5x}$ is continuous on [0, 1] and differentiable on (0, 1), so yes, the MVT is satisfied.

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