Question

tan^3 theta - tan ^2 theta +tan theta -1 = sec ^2 theta (tan theta -1)

Answer 1

RHS=sec² teta(tan teta-1)

AS sec² teta=tan² teta+1

=tan² teta+1(tan teta-1)

=tan³ teta-tan² teta+tan teta-1=LHS

Hence, proved.

Answer 2

tan³A-tan²A+tanA-1=sec²A(tanA-1)

Take RHS

(tan²A + 1)(tan A-1)

tan³A-tan²A+tan A-1

LHS

RHS = RHS