Question

sin theeta( 1 + tan theeta) + cos theeta( 1 + cot theeta) = sec theeta+cosec theeta

Answer 1

answer of question is above

Answer 2

we have to show

sinx(1+tanx)+cosx(1+cotx)=secx+cosecx

aking LHS

sinx(1+sinx/cosx) +cosx(1+cosx/sinx)

=sinx((cosx+sinx)/cosx) + cosx((sinx+cosx)/sinx)

=(sinx+cosx)(sinx/cosx+cosx/sinx)         taking sinx+cosx common

=sinx+cosx(sin**2x+cos**2x)/sinxcosx

=sinx+cosx/sinxcosx                  (sin**2x+cos**2x=1)

=sinx/sinxcosx+cosx/sinxcosx

=1/cosx+1/sinx

=secx+cosecx