Math, asked by sakshigaulechha0376, 1 year ago

cotA+cosecA-1/cotA-cosecA+1=1+cosA/sinA

Answers

Answered by Anonymous
4

SOLUTION:-

Take L.H.S

 \frac{cot \: A + cosec \: A  - 1}{cot \: A - cosec \: A + 1}  \\  \\  =  >  \frac{cot \: A + cosec \: A - ( {cosec}^{2} A -  {cot}^{2} A)}{cot \: A - cosec \: A + 1} \:  \:  \:  \:  \:  \: [ {cosec}^{2}  \theta -  {cot}^{2}   \theta = 1]\\  \\  =  >  \frac{(cot \: A + cosec \: A) - (cosec \: A - cot \: A)(cosec \: A + cot \: A)}{cot \: A - cosec \: A + 1}  \\  \\  =  >  \frac{(cosec \: A + cot \: A)[(1 - (cot \: A - cosec \: A)]}{cot \: A - cosec \: A + 1}  \\  \\  =  >  \frac{(cosec \: a + cot \: a)[cot \: A - cosec \: A + 1]}{cot \: A - cosec \: A + 1}  \\  \\  =  > cosec \: A + cot \: A \\  \\  =  >  \frac{1}{sin \: a}  +  \frac{cos \: A}{sin \: A}  \\  \\  =  >  \frac{1 + co s \: A}{sin \: A}  \:  \:  \:  \:  \:  \: [R.H.S]

Hope it helps ☺️

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