Question

(sinx + cos x) (sec x + cosec x) =2 + sec x cosec x

Answer 1

Hope this will help you.

LHS

(sinx+cosx) (secx+cosecx)

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

(sinx+cosx) (sinx+cosx/cosxsinx)

((sinx+cosx)^2/(cosxsinx)

(sin^2x+cos^2x+2sinxcosx/(cosxsinx)

1+2sinxcosx/(cosxsinx)

(1/cosxsinx+2sinxcosx/(cosxsinx)

=secx cosecx+2

2+secxcosecx=RHS

L.H.S=R.H.S

Answer 2

Hey there!

LHS=(sinx+cosx)(secx+cosecx)

=(sinx+cosx)(1cosx+1sinx)

=(sinx+cosx)(sinx+cosxcosxsinx)

=((sinx+cosx)2cosxsinx)

=(sin2x+cos2x+2sinxcosxcosxsinx)

=1+2sinxcosxcosxsinx

=(1cosxsinx+2sinxcosxcosxsinx)

=secxcosecx+2

=2+secxcosecx=RHS

Hope it Helps You!