tan 0 / 1 – cot 0 + cot 0 / 1 – tan 0 = 1 + sec cosec [Hint : Write the expression in terms of sine and cos 0]​

Question

tan 0 / 1 – cot 0 + cot 0 / 1 – tan 0
= 1 + sec cosec
[Hint : Write the expression in terms of sine and cos 0]​

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Skylar 1 month 2021-08-20T20:21:08+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-08-20T20:22:41+00:00

    Step-by-step explanation:

    solution starts from 1st page

    0
    2021-08-20T20:22:53+00:00

     LHS = \frac{tan 0}{1-cot 0} + \frac{cot 0}{ 1 - tan 0 }

     = \frac{\frac{sin 0}{cos 0}}{1 - \frac{cos 0}{sin 0}} + \frac{\frac{cos 0 }{sin 0}}{1 - \frac{sin 0}{cos 0}}

     = \frac{sin^{2} 0}{cos 0(sin 0 - cos 0)} + \frac{ cos^{2} 0}{ sin 0(cos 0 - sin 0) }

     = \frac{sin^{2} 0}{cos 0(sin 0 - cos 0)} - \frac{ cos^{2} 0}{ sin 0 (sin 0 - cos 0) }

     = \frac{sin^{3} 0 - cos^{3} 0}{ sin 0 cos 0 (sin 0 - cos 0) }

     = \frac{ (sin 0 - cos 0) ( sin^{2} 0 + sin 0 cos 0 + cos^{2} 0 ) }{ sin 0 cos 0 ( sin 0 - cos 0)}

     = \frac{ 1+sin 0 cos 0 }{ sin 0 cos 0 }

     = \frac{1}{sin 0 cos 0 } + \frac{sin 0 cos 0}{sin 0 cos 0 }

     = Cosec 0 sec 0 + 1

     = RHS

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