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UKProve that sin0(1+ tane) + cos(1 + cot8) sece + cosec

Answer»

Let theta = xLHS:sinx(1 + tanx) + cosx(1 + cotx)= sinx(cosx + sinx)/cosx + cosx(sinx + cosx)/sinx= (sinx + cosx)[sinx/cosx + cosx/sinx]=(sinx + cosx) [(sin^2 x + cos^2 x) /sinx. cosx]= (sinx + cosx) /sinx. cosx= 1/cosx + 1/sinx= secx + cosecx= RHS

Hence proved

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