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Prove that Tan∅/1-cot∅+cot∅ 1-tan∅=1+sec∅cosec∅

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Prove that Tan∅/1-cot∅+cot∅ 1-tan∅=1+sec∅cosec∅

Posted by Likith Parikh 1 year, 10 months ago

CBSE > Class 10 > Mathematics

1 answers

Saksham Dogra 1 year, 10 months ago

1−cotθ tanθ + 1−tanθ cotθ = 1− tanθ 1 tanθ + 1−tanθ tanθ 1 = tanθ tanθ−1 tanθ + tanθ(1−tanθ) 1 = tanθ−1 tan 2 θ + tanθ(1−tanθ) 1 = tanθ−1 tan 2 θ − tanθ(tanθ−1) 1 = tanθ(tanθ−1) tan 3 θ−1 = tanθ(tanθ−1) (tanθ−1)(tan 2 θ+tanθ+1) = tanθ tan 2 θ+tanθ+1 = tanθ tan 2 θ + tanθ tanθ + tanθ 1 =tanθ+1+cotθ =1+ cosθ sinθ + sinθ cosθ =1+ sinθcosθ sin 2 θ+cos 2 θ =1+ sinθcosθ 1 =1+secθcosecθ = RHS

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