SOLUTION: sin(A+B) = sin A cos B + cos A sin B cos(A+B) = cos A cos B - sin A sin B a) obtain an expression for cos 2x in terms of sin^2 x. b) obta

Question 181996: sin(A+B) = sin A cos B + cos A sin B
cos(A+B) = cos A cos B - sin A sin B
a) obtain an expression for cos 2x in terms of sin^2 x.
b) obtain an expression for sin 2x in terms of sin x and cos x.
c) show that cos 4x = 1 - 8sin^2 x + 8sin^4 x.
d) solve, for 0≤x≤π/2, the equation sin^2 x - sin^4 x = 0.1, giving your solutions to 2 decimal places.
e) find ∫(sin^4 x � sin^2 x + 2 cosx)dx. upper limit is π/2.
lower limit is 0.
Answer by vleith(2983) (Show Source): You can put this solution on YOUR website!
a)obtain an expression for cos 2x in terms of sin^2 x
cos(A+B) = cos A cos B - sin A sin B
Let A = x and B = x
cos(x+x) = cos x cos x - sin x sin x
cos(2x) = cos^2(x) - sin^2(x)
We know sin^2(x) + cos^2(x) = 1
So
cos(2x) = cos^2(x) - sin^2(x)
cos(2x) = (1-sin^2(x)) - sin^2(x)
cos(2x) = 1-2sin^2(x)
Use this URL to verify your answers --> http://www.sosmath.com/trig/Trig5/trig5/trig5.html
b) is a lot like a. You can do that one

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