Prove the following using trigonometric identities
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Thetha will be represented by A here onwards.
L.H.S=> cotA + cosecA -(cosec^2A - cot^2A)/cotA-cosecA+1
=cotA+cosecA-([cosecA+cotA][cosecA-cotA])/cotA-cosecA+1
=cotA+cosecA (1-[cosecA-cotA])/cotA-cosecA+1
=cotA+cosecA (1-cosecA+cotA)/cotA-cosecA+1
=cotA+cosecA=cosA/sinA+1/sinA=cosA+1/sinA=R.H.S
Hence, proved.
L.H.S=> cotA + cosecA -(cosec^2A - cot^2A)/cotA-cosecA+1
=cotA+cosecA-([cosecA+cotA][cosecA-cotA])/cotA-cosecA+1
=cotA+cosecA (1-[cosecA-cotA])/cotA-cosecA+1
=cotA+cosecA (1-cosecA+cotA)/cotA-cosecA+1
=cotA+cosecA=cosA/sinA+1/sinA=cosA+1/sinA=R.H.S
Hence, proved.
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