Math, asked by mosisk700, 9 months ago

prove that.
cot²A(1-cos²A)=cos²A​

Answers

Answered by deekshantsinghal7996
0

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.

Answered by Anonymous
7

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.

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