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Implicit Differentiation

Sin theta +si...

Question

Sin theta + sin 2theta + sin 3theta =sin alpha and cos theta + cos 2theta + cos 3theta= cos alpha, then theta is equal to

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Solution

SinA+sin3A+sin2A=sinB 2sin(A+3A)/2cos(3A-A)/2+sin2A=sinB 2sin2AcosA+sin2A=sinB-----(1) Similarly in case of cos 2cos2A*cosA+cos2A=cosB------(2) Dividing 1&2 Sin2A(cosA+1)/cos2A(cosA+1)=sinB/cosB tan2A=tan B 2A=B

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