Answer :

We have, secθ = 5/4 = 1/cosθ


cosθ = (4k)/(5k) = AC/AB (For some value of k)



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


AB2 = BC2 + AC2


= (5k)2 = BC2 + (4k)2


= 25k2 = BC2 + 16k2


= BC2 = 9k2


BC = 3k


sinθ = BC/AB = (3k)/(5k) = 3/5


consider the LHS


LHS = =


=


=


=


=


= 12/7


= RHS


HENCE PROVED


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