(1+cotA-cosecA)(1+tanA+secA)=2
Hello the answer is too long to type so to solve the question you have to first convert the given ratios into sin and Cos and then open the bracket and you will get the answer
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(1+cot A-cosec A).(1+tanA+secA)= 2L.H.S.=(1+cosA/sinA-1/sinA).(1+sinA/cosA+1/cosA)=(sinA+cosA-1)×(cosA+sinA+1)/sinA.cosA)=[(sinA+cosA)^2-(1)^2]/sinA.cosA.=(sin^2A+cos^2A+2.sinA.cosA-1)/sinA.cosA.=( 1+2.sinA.cosA -1)/sinA.cosA.= 2.sinA.cosA/sinA.cosA= 2 =R.H.S (proved)