Math, asked by letnee8142, 1 year ago

Cot theta is equal to 7 by 8 then find 1+sin theta by cos theta

Answers

Answered by anshpal629
2

Answer:

 \frac{ \sqrt{113}  + 8}{7}

Step-by-step explanation:

 \cot( \alpha )  =  \frac{7}{8}  =  \frac{b}{p}  \\  b = 7x \\ p = 8x \\ therefore \:  \\  {h}^{2}  =  {p}^{2}  +  {b}^{2}  \\ h =  \sqrt{ {p}^{2} +   {b}^{2}   }  \\  \:  \:  \:  \:  =  \sqrt{ {8}^{2} +  {7}^{2}  }  \\  \:  \:  \:  \:  =  \sqrt{64 + 49 } \\  \:  \: \:   \:  =   \sqrt{113}  \\  sin( \alpha )  =  \frac{p}{h}  =  \frac{8}{ \sqrt{113} }  \\  \cos( \alpha )  =  \frac{b}{h}  =  \frac{7}{ \sqrt{113} }   \\  \:  \:  \:  \:  =  \frac{1 +  \sin( \alpha ) }{ \cos( \alpha ) }  \\  \:  \:  \:  =  \frac{1 +  \frac{8}{ \sqrt{113} } }{ \frac{7}{ \sqrt{113} } }  \\  \:  \:  \:  =    \frac{ \frac{ \sqrt{113 + 8} }{ \sqrt{113} } }{ \frac{7}{ \sqrt{113} } }  \\  \:  \:  \:  \:  =  \frac{  \sqrt{113}   + 8}{ \sqrt{113} }  \times  \frac{ \sqrt{113} }{7}  \\  \:  \:  \:  =  \frac{ \sqrt[1]{113} }{7}

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