sin*sin=1.732*sinx*cos2x
To understand and solve the equation sin(sin x) = 1.732 sin x cos(2x), we will break it down step by step.
1. Start with the equation: sin(sin x) = 1.732 sin x cos(2x)
2. We notice that the equation involves trigonometric functions. To simplify, use the trigonometric identity sin(2x) = 2sin x cos x. We can apply this identity to the equation.
sin(sin x) = 1.732 sin x cos(2x)
sin(sin x) = 1.732 sin x * 2sin x cos x
3. Simplify further:
sin(sin x) = 3.464 sin^2 x cos x
4. Now, let's focus on the left side of the equation, sin(sin x). Since the inner sin is in radians, we can rewrite the equation as:
sin y = 3.464 sin^2 x cos x, where y = sin x
5. Next, we square both sides of the equation to eliminate the square root:
sin^2 y = (3.464 sin^2 x cos x)^2
sin^2 y = 11.98 sin^4 x cos^2 x
6. We can simplify further by recognizing that sin^2 x = 1 - cos^2 x from the Pythagorean identity. Rearrange this identity to get: sin^2 x = 1 - cos^2 x.
7. Substitute this identity into the equation:
sin^2 y = 11.98 (1 - cos^2 x) cos^2 x
8. Distribute the 11.98 term:
sin^2 y = 11.98 cos^2 x - 11.98 cos^4 x
9. Rearrange the equation to bring all terms to one side:
11.98 cos^4 x - 11.98 cos^2 x + sin^2 y = 0
10. Notice that we have converted the original equation into a polynomial equation in terms of cos x. This can be solved using numerical methods or factoring, depending on the complexity and constraints of the problem.
These steps outline how to simplify the equation involving sin(sin x) = 1.732 sin x cos(2x) and convert it into a polynomial equation in terms of cos x. Further solving the equation requires additional steps such as finding the roots or applying numerical methods.