Question

prove that.
cot²A(1-cos²A)=cos²A​

Answer 1

Answer:

$\cot {}^{2} (a) (1 - \cos {}^{2} (a) ) \\ \\ cot {}^{2} \alpha = \frac{ \cos {}^{2} ( \alpha ) }{ \sin {}^{2} \alpha ) } \: \: \: \: \\ \\ 1 = \cos {}^{2} ( \alpha ) + \sin {}^{2} ( \alpha ) \\ using \: them \: \\ \\ \frac{ \cos {}^{2} ( a) }{ \sin {}^{2} (a) } \times \sin {}^{2} (a) \\ \\ \\ \cos {}^{2} (a)$

So LHS = RHS.

Answer 2

Answer:

To prove :

cot^2 A( 1 - cos^2 A ) = cos^2 A

.... (1)

Proof :

We know that,

cot A = cos A / sin A .... (2)

sin^2 A = (1-cos^2A) .....(3)

Then,

By taking L. H. S. , of the given equation i. e. From eq. (1) , we get,

cot^2 A( 1 - cos^2 A ) =

= cot^2 A × (sin^2 A)

{from eq. (3)}

= (cos^2 A / sin^2 A) × (sin^2 A)

{from eq. (2)}

= cos^2 A = R. H. S. of eq. (1)

L. H. S. of eq. (1) = R. H. S of eq. (1)

L. H. S. = R. H. S.

Hence proved.