If tanθ = 20/21, show that

We have, tanθ = (20k)/(21k) = BC/AC (For some value of k)



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


AB2 = BC2 + AC2


= AB2 = (20k)2 + (21k)2


= AB2 = 400k2 + 441k2


= AB2 = 841k2


= (29k)2


AB = 29k


sinθ = BC/AB = (20k)/(29k) = 20/29


cosθ = AC/AB = (21k)/(29k) = 21/29


consider, the LHS


LHS = =


=


= 30/70


= 3/7


= RHS


HENCE PROVED


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