Solve the equation 3sinx-cos2x=1 for 0 x=30 x=150
By writing sin3x as sin(x+2x), show that sin3x=3sinx-4sin^3x for all values of x?
To prove this, we need to use the following formulas: sin(A + B) = sin(A)cos(B) + cos(A)sin(B) cos(2x) = 1 - 2sin²(x) sin(2x) = 2sin(x)cos(x) cos²(x) = 1 - sin²(x). With A = x and B = 2x in the first formula, we have: sin(3x) => sin(x + 2x) = sin(x)cos(2x) + cos(x)sin(2x) = sin(x)[1 - 2sin²(x)] + cos(x)[2sin(x)cos(x)] = sin(x) - 2sin³(x) + 2sin(x)cos²(x) = sin(x) - 2sin³(x) + 2sin(x)[1 - sin²(x)] = sin(x) - 2sin³(x) + 2sin(x) - 2sin³(x) = 3sin(x) - 4sin³(x), as required. I hope this helps!
Solve each equation maths help?!?
2 points does not harm you
How would you solve sin3x = 3sinx + 4sin^3x?
I think you mean how would you prove... not solve. Recall: sin (A + B) = sin A cos B + cos A sin B sin 2x = 2 sin x cos x cos 2x = cos^2 x - sin^2 x = 2 cos^2 x - 1 = 1 - 2 sin^2 x sin^2 x + cos^2 x = 1 sin 3x = sin (2x + x) = sin 2x. cos x + cos 2x. sin x = 2 sin x cos x. cos x + (1 - 2 sin^2 x) . sin x = 2 sin x cos x. cos x + sin x - 2 sin^3 x = 2 sin x cos^2 x + sin x - 2 sin^3 x = 2 sin x (1 - sin^2 x) + sin x - 2 sin^3 x = 2 sin x - 2 sin^3 x + sin x - 2 sin^3 x = 3 sin x - 4 sin^3 x. I hope that helps. :) me07.