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If `Tan θ = 20/21` Show that `(1 - Sin Theta + Cos Theta)/(1 + Sin Theta + Cos Theta) = 3/7` - CBSE Class 10 - Mathematics

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Question

If `tan θ = 20/21` show that `(1 - sin theta + cos theta)/(1 + sin theta + cos theta) = 3/7`

Solution

`tan theta = "Opposite side"/"efficient side" = 20/21`

Let x be the hypotenuse By applying Pythagoras we get

`AC^2 + AB^2 + BC^2`

`x^2 = (20)^2 + (21)^2`

`x^2 = 400 + 441`

`x^2 = 840 => x = 29`

`sin theta = (AB)/(AC) = 20/29`

`cos theta = (BC)/(AC) = 21/29`

Substitute sin θ, cos θ in equation we get

`=> (1 - sin theta + cos theta)/(1 + sin theta + cos theta)`

`=> (1 - 20/29 + 21/29)/(1 + 20/29 + 21/29) = ((29 - 20 + 21)/29)/((29 + 20 + 21)/29) = 30/70 = 3/7`

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Solution If `Tan θ = 20/21` Show that `(1 - Sin Theta + Cos Theta)/(1 + Sin Theta + Cos Theta) = 3/7` Concept: Trigonometric Ratios.
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