Math, asked by aamirkhan9548687102, 2 months ago

COS 45°
sec 30° + cosec 30°​

Answers

Answered by sandy1816
13

 \frac{cos45 \degree}{sec30 \degree + cosec30 \degree}  \\  \\  =  \frac{ \frac{1}{ \sqrt{2} } }{ \frac{2}{ \sqrt{3} } + 2 }  \\  \\  =  \frac{1}{ \sqrt{2} }  \times  \frac{ \sqrt{3} }{ 2 + 2 \sqrt{3} }  \\  \\  =  \frac{ \sqrt{3} }{2 \sqrt{2}  + 2 \sqrt{6} }  \\  \\  =  \frac{ \sqrt{3} }{2 \sqrt{2}  + 2 \sqrt{6} }  \times  \frac{2 \sqrt{2}  - 2 \sqrt{6} }{2 \sqrt{2} - 2 \sqrt{6}  }  \\  \\  =  \frac{2 \sqrt{6}  - 2 \sqrt{18} }{8 - 24}  \\  \\  =  \frac{2 \sqrt{6}  - 6 \sqrt{2} }{ - 16}  \\  \\  =  \frac{3 \sqrt{2}  -  \sqrt{6} }{8}

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