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  • Prove the following : 1+cot power 2 alpha by 1+cosec alpha = cosec alpha

Prove the following :

1+\frac{\cot ^{2}\alpha }{1+\cos ec\alpha }= \cos ec\, \alpha

Answers (1)

1+\frac{\cot ^{2}\alpha }{1+\cos ec\alpha }= \cos ec\, \alpha

Taking L.H.S.
           = 1+\frac{\cot ^{2}\alpha }{1+\cos ec\, \alpha }  
          
          = \frac{1+\cos ec\, \alpha +\cot ^{2}\alpha }{1+\cos ec\, \alpha }
        = \frac{\cos ec^{2}\alpha-\cot ^{2}\alpha+ \cos ec\, \alpha+\cot ^{2}\alpha \, \, }{1+\cos ec\, \alpha }      \left ( \because \cos ec^{2}\theta -\cot ^{2}\theta = 1 \right )
       = \frac{\cos ec^{2}\alpha +\cos ec\, \alpha }{1+\cos ec\, \alpha }
      = \frac{\cos ec\, \alpha \left ( \cos ec\, \alpha+1 \right ) }{\left ( 1+\cos ec\, \alpha \right )}
     = \cos ec\, \alpha
 L.H.S. = R.H.S.
Hence proved

Posted by

infoexpert27

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