evaluate (1+cotx-cosecx)(1+tanx+secx) please answer quickly
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Step-by-step explanation:
(1+cotx-cosecx)(1+tanx+secx)
= (1 + cosx/sinx - 1/sinx)(1 + sinx/cosx + 1/cosx)
= {(sinx + cosx - 1)/sinx} × {(cosx + sinx + 1)/cosx}
= {(sinx + cosx)^2 - 1^2}/(sinx × cosx)
= (sin^2 x + cos^2 x + 2 × sinx × cosx - 1)/(sinx × cosx)
= (1 + 2sinxcosx -1)/sinxcosx
= 2sinxcosx/sinxcosx
= 2
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