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प्रश्न
In a right-angled triangle, it is given that A is an acute angle and tan A = `(5) /(12)`.
find the value of :
(i) cos A
(ii) sin A
(iii) ` (cosA+sinA)/(cosA– sin A)`
उत्तर
Consider the diagram below :
tan A = `(5)/(12)`
i.e.`"perpendicular"/"base" = (5)/(12) ⇒ "BC"/"AB" = (5)/(12)`
Therefore if length of AB = 12x, length of BC = 5x
Since
AB2 + BC2 = AC2 ...[ Using Pythagoras Theorem ]
(12x)2 + (5x)2 = AC2
AC2 = 144x2 + 25x2
AC2 = 169x2
∴ AC = 13x ...( hypotenuse)
(i) cos A = `"base"/"hypotenuse" = "AB"/"AC" = (12x)/(13x) = 12/13`
(ii) sin A = `"perpendicular"/"hypotenuse" = (5x)/(13x) = 5/13`
(iii) `(cos "A" + sin "A")/(cos "A" – sin "A")`
= `(12/13+5/13)/(12/13 – 5/13)`
= `(17/13)/(17/7)`
= `17/7`
= `2(3)/(7)`
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