Question

if sin teta+Cos teta=a and tan teta+cot teta=b,then b(a square-1)

Answer 1

b=tan theta+cot theta

  =sin theta/cos theta+cos theta/sin theta

=sin^2 theta+cos^2 theta/sin theta*cos theta

=1/sin theta*cos theta

a=sin theta+cos theta

b*(a^2-1)=1/sin theta*cos theta(1+2sin theta*cos theta-1)

            =2

Answer 2

tan@+cot@ [(sin@+cos@)^2 -1]

= tan@+cot@ (sin^2@+cos^2@+2sin@cos@ -1)

=cot@+tan@(1+2sin@cos@-1)

=cot@+tan@(2sin@cos@)

convert cot and tan in sin and cos terms

ie. sin@/cos@ + cos@/sin@ (2sin@cos@)

taking l.c.m.

=sin^2@+cos^2@ x(2sin@cos@)

_________________

sin@cos@

cancel sin@cos@

=1(2) = 2