Q. 153.7( 13 Votes )

If sinθ = 3/4, sh

Answer :

We have, sinθ = (3k)/(4k) = BC/AB (For some value of k)


Consider the LHS


LHS = =


=


=


= cosθ /sinθ


= cotθ



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


AB2 = BC2 + AC2


= (4k)2 = (3k)2 + AC2


= 16k2 = 9k2 + AC2


= AC2 = 7k2


AC = k√7


cotθ = AC/BC = k/(k√7) = 1/√7


LHS = RHS


HENCE PROVED


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