Question

1/tanA+cotA =cosA sinA​

Answer 1

Answer:

Step-by-step explanation:

Given:

> 1/tan A + cot A = cos A sin A

Considering the L.H.S:

=> 1/tan A + cot A

We know:

=> tan A = sin A/cos A

=> cot A = cos A/sin A

Hence, we get:

=> 1/(sin A/cos A) + (cos A/sin A)

Taking L.C.M we get:

=> 1/(sin² A + cos² A)/sin A × cos A

We know:

=> sin² A + cos² A = 1

So, we get:

=> 1/(1/sin A × cos A)

=> sin A cos A or cos A sin A.

Hence, L.H.S = R.H.S.

Answer 2

$\dfrac{1}{ \tan(A) + \cot(A) }$

$\dfrac{1}{ \frac{ \sin(A) }{ \cos(A) } + \frac{ \cos(A) }{ \sin(A) } } = \dfrac{1}{ \frac{ \sin^{2} (A) + \cos^{2} (A) }{ \sin(A) \cos(A) } }$

$= \dfrac{ \sin(A) \cos(A) }{ \sin^{2} (A) + \cos^{2} (A) }$

$= \boxed{ \sin(A) \cos(A) }$