Question

Cot (45-a )=cos2a/1-sin2a

Answer 1

Hi ,

Cot( A - B )

= ( CotA cotB+1 ) / ( cotB-cotA)

Now ,

LHS = cot( 45 - A )

= ( CotAcot45° + 1 )/( cotA - cot45 )

= ( CotA +1 ) /( cotA - 1 )

= ( CosA/sinA + 1 )/( cosA/sinA - 1 )

= ( CosA + sinA ) / ( cosA - sinA )

= (CosA+sinA)²/(cosA+sinA)(cosA-sinA)

= (cos²A+sin²A+2sinAcosA)/(cos²A-sin² A)

= (1 + 2sinAcosA) / cos2A

= ( 1 + sin2A ) /cos2A

I hope this helps you.

:)