TRIG..............
posted by MATHS on .
Q.1 Prove the following identities:
(i) tan^3x/1+tan^2x + cot^3x/1+cot^2 = 12sin^x cos^x/sinx cosx
(ii) (1+cotx+tanx)(sinxcosx)/sec^3xcosec^3x = sin^2xcos^2x.

without brackets the first one is much too ambiguous to attempt.
even the second one, I will fix so it works
LS = (1+cotx+tanx)(sinxcosx)/(sec^3xcosec^3x)
= (1 + cosx/sinx + sinx/cosx)(sinxcosx)/(sec^3xcosec^3x)
= sinx  cosx + cosx  cos^2x + sin^2x  sinx)/(1/cos^3x  1/sin^3x)
= ((sin^2x/cosx  cos^2x/sinx)/((sin^3x  cos^3x)/(sin^3xcos^3x))
= (sin^3x  cos^3x)/(sinxcosx) (sin^3xcos^3x)/(sin^3cos^3x)
= sin^2xcos^2x
= RS