Answer :

We have, cosθ = (7k)/(25k) = base/hypotenuse (For some value of k)



By Pythagoras theorem, (hypotenuse)2 = (perpendicular)2 + (base)2


AB2 = BC2 + AC2


= (25k)2 = BC2 + (7k)2 (for some value of k)


= 625k2 = BC2 + 49k2


= BC2 = 576k2


= BC2 = (24k)2


BC = 24k


Hence, the trigonometric ratios of the given θ are:


sinθ = BC/AB = (24k)/(25k) = 24/25


cosθ = 7/25


tanθ = BC/AC = sinθ /cosθ = 24/7


cotθ = AC/BC = 1/tanθ = 7/24


cosecθ = AB/BC = 1/sinθ = 25/24


secθ = AB/AC = 1/cosθ = 25/7


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