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Prove that tanθ−cotθ=
sinθcosθ
2sin
2
θ−1
.
Medium
Solution
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LHS=tanθ−cotθ
=
cosθ
sinθ
−
sinθ
cosθ
=
sinθcosθ
sin
2
θ−cos
2
θ
=
sinθcosθ
sin
2
θ−(1−sin
2
θ)
=
sinθcosθ
2sin
2
θ−1
=RHS
Hence proved
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Answer:
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Step-by-step explanation:-
⇒ Cosθ (1 - 2cos²θ) / sinθ (2sin²θ - 1)
⇒ Cosθ (1 - 2(1 - sin²θ) / sinθ(2sin²θ - 1)
⇒Cosθ (2sin²θ - 1) / sinθ(2sin²θ - 1)
∴ Cosθ / sinθ = cotθ
LHS = RHS
Hence proved
Additional information:-
(1) sin²θ + Cos²θ = 1
(2) Cosθ / sinθ = cotθ
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