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KonstantinChe [14]
2 years ago
15

(a) If tan A=x/yprove that: y.cos2A +x.sin2A= y.Please help me..​

Mathematics
1 answer:
katrin2010 [14]2 years ago
4 0

Answer:  see proof below

<u>Step-by-step explanation:</u>

Use the following Double Angle Identities: cos 2A = 1 - 2sin²A

                                                                        sin 2A = 2sinA · cosA

\text{Given:}\quad \tan A = \dfrac{x}{y}

<u>Proof LHS = RHS</u>

y cos 2A + x sin 2A = y

                  x sin 2A = y - y cos 2A

                  x sin 2A = y(1 - cos 2A)

                  \dfrac{x}{y}=\dfrac{1-\cos2A}{sin\ 2A}

                  \dfrac{x}{y}=\dfrac{1-(1-2sin^2A)}{2\sin A\cdot \cos A}

                  \dfrac{x}{y}=\dfrac{2sin^2A}{2\sin A\cdot \cos A}

                  \dfrac{x}{y}=\dfrac{\sin A}{\cos A}

                  \dfrac{x}{y}=\tan A}

This is a TRUE statement since it was given that  \tan A = \dfrac{x}{y}  

                     

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