Question

please help fast....​

Answer 1

Solution

Show That :-

• (cot A)/(1-cot A) + (tan A)/(1-tan A) = -1

Explanation

Take L.H.S.

= (cot A)/(1-cot A) + (tan A)/(1-tan A)

We Have,

$\star\tt{\red{\:\cot\theta\:=\:\dfrac{\cos\theta}{\sin\theta}}}$

$\star\tt{\orange{\:\tan\theta\:=\:\dfrac{\sin\theta}{\cos\theta}}}$

Keep all above Values,

= [(cos A/sin A)/{1 - (cos A/sin A)} ] + [(sin A/cos A)/{1 - (sin A/cos A)}]

= cos A/(sin A - cos A) + sin A/(cos A - sin A)

Take (-) sign common from denominator of second part

= cos A/(sin A - cos A) - sin A/(sin A - cos A)

Take (sin A - cos A) L.C.M.

= ( cos A - sin A )/(sin A - cos A)

Take (-) Common from numerator

= -(sin A - cos A)/(sin A - cos A)

= -1

= R.H.S.

That's Proved.

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