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cos((pi)/(2)-.578)sin(.578)+cos(.578)sin((pi)/(2)-.578)

cos⁡(π2−.578)sin⁡(.578)+cos⁡(.578)sin⁡(π2−.578) \cos \left(\frac{\pi}{2}-.578\right) \sin (.578)+\cos (.578) \sin \left(\frac{\pi}{2}-.578\right)

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Divide polynomials using long divisionright chevron icon

Full solution

Q. cos⁡(π2−.578)sin⁡(.578)+cos⁡(.578)sin⁡(π2−.578) \cos \left(\frac{\pi}{2}-.578\right) \sin (.578)+\cos (.578) \sin \left(\frac{\pi}{2}-.578\right)
  1. Apply Co-function Identities: Use the co-function identities: cos⁡(π2−x)=sin⁡(x)\cos(\frac{\pi}{2} - x) = \sin(x) and sin⁡(π2−x)=cos⁡(x)\sin(\frac{\pi}{2} - x) = \cos(x).
    cos⁡((π2)−0.578)sin⁡(0.578)+cos⁡(0.578)sin⁡((π2)−0.578)=sin⁡(0.578)sin⁡(0.578)+cos⁡(0.578)cos⁡(0.578)\cos(\left(\frac{\pi}{2}\right) - 0.578)\sin(0.578) + \cos(0.578)\sin(\left(\frac{\pi}{2}\right) - 0.578) = \sin(0.578)\sin(0.578) + \cos(0.578)\cos(0.578)
  2. Calculate Values: Calculate the values of sin⁡(0.578)sin⁡(0.578)\sin(0.578)\sin(0.578) and cos⁡(0.578)cos⁡(0.578)\cos(0.578)\cos(0.578).sin⁡(0.578)sin⁡(0.578)+cos⁡(0.578)cos⁡(0.578)=sin⁡2(0.578)+cos⁡2(0.578)\sin(0.578)\sin(0.578) + \cos(0.578)\cos(0.578) = \sin^2(0.578) + \cos^2(0.578)
  3. Use Pythagorean Identity: Use the Pythagorean identity: sin⁡2(x)+cos⁡2(x)=1\sin^2(x) + \cos^2(x) = 1.\newlinesin⁡2(0.578)+cos⁡2(0.578)=1\sin^2(0.578) + \cos^2(0.578) = 1
  4. Conclude Calculation: Conclude the calculation.\newlineThe final answer is 11.

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