Question

sinx+cosx) (secx+cosecx)= 2+secx cosecx

Answer 1

(sinx +cosx)(secx+cosecx)
(sinx+cosx)(1/cos+1/sin)
(sinx+cosx)(sin+cos)/sincos
((sinx+cosx)^2)sinxcosx
(sinx^2+cosx^2+2sinxcosx)/sinxcosx
(1+2sinxcosx)/sinxcosx
1/sinxcosx+2sinxcosx/sinxcosx
cosecxsecx+2
2+cosecxsecx
lhs=rhs

Answer 2

(sinx+cosx)((1/cosx)+(1/sinx))
(sinx+cosx)(sinx+cosx)/sinxcosx
(sinx+cosx)²/sinxcosx
(sin²x+cos²x+2sixcosx)/sinxcosx
(1+2sinxcosx)/sinxcosx
((1/sinxcosx)+2)
2+secxcosecx