prove that (cosec theta - sec theta) (cot thata-tan theta)=(cosec theta+sec theta)(sec theta cosec theta-2)
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LHS=(cosecθ−secθ)(cotθ−tanθ).
=(
sinθ
1
−
cosθ
1
)+(
sinθ
cosθ
−
cosθ
sinθ
)
=(
sin
2
θcos
2
θ
(cosθ−sinθ)(cos
2
θ−sin
2
θ)
)
=(
sin
2
θcos
2
θ
(cosθ−sinθ)
2
(cosθ+sinθ)
)
=(
sin
2
θcos
2
θ
(1−2cosθsinθ)(cosθ+sinθ)
)
=(
(sinθcosθ)(sinθcosθ)
(1−2cosθsinθ)(cosθ+sinθ)
)
=(cosecθsecθ−2)(cosecθ+secθ)
=RHS
Hence proved
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