Math, asked by harshaldulera82, 1 year ago

If y = a sin x + b cos x, find dy/dx when tan x =a/b

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Answered by ravisimsim
9

Answer:

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Answered by sandy1816
1

tanx =  \frac{a}{b}  \\  \\  {sec}^{2} x = 1 +  {tan}^{2} x \\ secx =  \sqrt{1 +  \frac{ {a}^{2} }{ {b}^{2} } }  \\  secx =  \frac{ \sqrt{ {a}^{2} +  {b}^{2}  } }{b}  \\  \\ cosx =  \frac{b}{ \sqrt{ {a}^{2}  +  {b}^{2} } }  \\  \\ sinx =  \sqrt{1 -  \frac{ {b}^{2} }{ {a}^{2}  +  {b}^{2} } }  \\ sinx =  \frac{a}{ \sqrt{ {a}^{2} +  {b}^{2}  } }  \\  \\  \\ y = asinx + bcosx \\ y = a \times  \frac{a}{ \sqrt{ {a}^{2} +  {b}^{2}  } }  + b \times  \frac{b}{ \sqrt{ {a}^{2} +  {b}^{2}  } }  \\ y =  \frac{ {a}^{2} }{ \sqrt{ {a}^{2} +  {b}^{2}  } }  +  \frac{ {b}^{2} }{ \sqrt{ {a}^{2}  +  {b}^{2} } }    \\ \\  \frac{dy}{dx} = 0

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