Homework Sourseverify sinxcosxsinxcotxsecxcscxcosxtanxSolutionsinx cosx s
verify sin(x)+cos(x)+sin(x)/cot(x)=sec(x)=csc(x)-cos(x)/tan(x)
Solution
sin(x) + cos(x) + sin(x)/cot(x) - sec(x) = csc(x) - cos(x)/tan(x)
LHS = sin(x) + cos(x) + sin(x)/cot(x) - sec(x) = sin(x) + cos(x) + sin^2(x)/cos(x) - sec(x)
= - sec(x) + [sin(x)*cos(x) + cos^2(x) + sin^2(x)]/cos(x) = - sec(x) + [sin(x)*cos(x) + 1]/cos(x) = sin x
RHS = csc(x) - cos(x)/tan(x) = 1/sin(x) - cos^2(x)/sin(x) = [1 - cos^2(x)]/sin(x) = sin(x)
LHS = RHS
