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प्रश्न
Prove that `(sin 70°)/(cos 20°) + (cosec 20°)/(sec 70°) - 2 cos 70° xx cosec 20°` = 0.
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उत्तर
LHS = `(sin 70°)/(cos 20°) + (cosec 20°)/(sec 70°) - 2 cos 70° xx cosec 20°`
= `sin (90° - 20°)/(cos 20°) + (cosec(90° - 20°))/(sec 70°) - 2 cos 70° xx cosec 20°`
= `(cos 20°)/(cos 20°) + (sec 70°)/(sec 70°) - 2 cos 70° xx cosec 20°`
= 1 + 1 - 2cos (90° - 20°) . cosec 20°
= 2 - 2 sin 20°. `1/sin 20°`
= 2 - 2
= 0
= RHS
Hence proved.
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`1/(tanA + cotA) = sinAcosA`
Prove that `(sin θ tan θ)/(1 - cos θ) = 1 + sec θ.`
If x = a sec θ + b tan θ and y = a tan θ + b sec θ prove that x2 - y2 = a2 - b2.
Prove that the following identities:
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Prove that identity:
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