Sintheta/cottheta+cosectheta-sintheta/cottheta -cosectheta =2
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Step-by-step explanation:
Let theta = α
Given LHS = Sintheta/cottheta+cosectheta - sintheta/cottheta -cosectheta
= sinα / (cotα + cosecα) - sinα / (cotα - cosecα)
= sinα {(cotα - cosecα) - (cotα + cosecα)} / (cotα - cosecα)(cotα + cosecα)
= sinα {cotα - cosecα - cotα - cosecα} / (cot²α - cosec²α)
= sinα (-2cosecα) / -1
= 2sinα / sinα = 2 = RHS
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