Question

if m sin theta+r cos theta=p and m cos theta-n sin theta=q,then prove that m^2+n^2=p^2+p^2

Answer 1

m Sin Ф + n Cos Ф  = p
     =>  m² Sin² Ф + n² Cos² Ф + 2 m n Sin Ф Cos Ф  = p²
m Cos Ф - n Sin Ф = q
     =>  m² Cos² Ф + n² Sin²Ф - 2 m n Sin Ф Cos Ф  = q²

add the two equations:

      m² (sin²Ф +Cos²Ф) + n²(sin²Ф+Cos²Ф)  =  p² + q²

m² + n² =  p² + q²

Answer 2

Step-by-step explanation: Please find the attachment...

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