14. () (sin x + cos x) (sec x + cosec x) = 2 + sec x cosec x
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Step-by-step explanation:
LHS= (sinx+cosx)(secx+cosecx)
=(sinx+cosx)(1/cosx+1/sinx)
=(sinx+cosx){(sinx+cosx)/sinx cosx}
=(sinx+cosx)²/sinxcosx
=(sin²x+cos²x+2sinxcosx)/sinxcosx
=2sinxcosx/sinxcosx + sin²xcos²x /
sinxcosx
= 2 + 1/sinxcosx
= 2 + secx cosecx
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