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If 1-sin theta+cos theta / 1+sin theta +cos theta = 3/7 prove that tan theta =20/21 |
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Answer» Answer: tanθ = 20/21 = opposite SIDE(o)/adjacent side(a) hypotenuse = h = o² + a² Let , o = 20K and a = 21k h² = (20k)² + (21k)² = 841k² h = 29 k sinθ = o/h = 20k/29k =20/29 cosθ = a/h = 21k/29k = 21/29 sinθ = o/h = 20k/29k =20/29 cosθ = a/h = 21k/29k = 21/29 1 - sinθ + cosθ ÷ 1 + sinθ + cosθ = {1 - 20/29 + 21/29 / 1 } ÷ {1 + 20/29 + 21/29} = {29/29 - 20/29 + 21/29) ÷ {29/29+20/29+21/29} = {29 - 20 + 21/29} ÷ {29+20+21/29} = 30/29 ÷ 70/29 29 gets cancelled on both denominator and NUMERATOR. = 30/70 = 3/7 = RHS Proved. |
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