Use the trigonometric identities to transform one side of th

Use the trigonometric identities to transform one side of the equation to the other (0

a) cot x sin x = cos x

simplifying the left hand side

cot x = cos x / sin x

so left side becomes

cos x / sin x * sin x

cos x = cos x

left hand side = right hand side

proved !

b) ( 1 + sin x ) ( 1 - sin x ) = cos^2 x

applying foil on left side to multiply

1 - sinx + sin x - sin^2 x

1 - sin^2 x

applying trigonometric identity

sin^2 x + cos^2 x = 1

( sin^2 x + cos ^2 x ) - sin^2 x

so we are left with cos^2 x on left side

hence,

cos^2 x = cos^2 x

proved !