cosxsecx sin x csc x sin x Verify algebraically that the e

cos(x)/sec(x) sin (x) = csc (x) - sin (x) Verify algebraically that the equation is an identity. Use a Reciprocal Identity to rewrite the expression in terms cos(x)/sec(x) sin(x) = cos(x)/1/cos(x) + sin(x) Use a Identity to rewrite the expression in terms Simplify. 3/sin(x) = (sin^2 (x)/sin(x)) csc (x) - sin (x)

Solution

cosx/( secxsinx)

= cosx/(1/cosx)*sinx

= cosx*cosx/sinx = cos^2x/sinx

Use a pythogorean------ sin^2x +cos^2x =1

= ( 1- sin^2x)/sinx

=1/sinx - ( sin^2x)/sinx

= cscx - sinx