prove that
(1/tan a)-(1/tan 2a) = cosec 2a
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Explanation:- From LHS 1/tana - 1/tan2a
- ∵ tana = sina/cosa
∴ 1/sina /cosa - 1/sin2a/cos2a
= cosa /sina - cos2a/sin2a
- ∵ sin2a = 2sina × cosa
- and cos2a = cos²a - sin²a
∴ cosa /sina - cos²a - sin²a /2sina cosa
= 2cos²a -(sin²a - cos²a)/2sinacosa
= cos²a + sin²a /sin2a
- As we know that , cos²a+sin²a = 1
= 1/sin2a = cosec2a
- LHS = RHS proved
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