CBSE Class 10 Answered

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2/  (1+tanθ + cotθ) (sinθ-cosθ) =(secθ/cosec²θ - cosecθ/sec²θ)

RHS =

(secθ/cosec²θ - cosecθ/sec²θ) =

(sec³θ -cosec³θ)/ cosec²θsec²θ =

(secθ -cosecθ)((sec²θ +secθ cosecθ + cosec²θ)/ cosec²θsec²θ =

Converting sec and cosec's into sin and cos,

[{(sinθ -cosθ)/(sinθcosθ)}{(tanθ +1 + cotθ)/(sinθcosθ)}]/ cosec²θsec²θ =

[{(sinθ -cosθ)(tanθ +1 + cotθ)}/(sinθcosθ)²]/ cosec²θsec²θ =

(sinθ -cosθ)(tanθ +1 + cotθ) = LHS.

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