If tan A=
, then sin A. cos A=
.
Given: 
And we know, 
So
⇒ perpendicular = 3k and base = 4k
By Pythagoras theorem, (hypotenuse)2 = (perpendicular)2 + (base)2
⇒ (hypotenuse)2 = (3k)2+ (4k)2 = 9k2+16k2 = 25k2
⇒ hypotenuse = 5k
[∵ (hypotenuse)2 = 25k2⇒ hypotenuse = √(25k2) = 5k)
Thus, sin A and cos A can be found out.
Multiplying sin A and cos A,
Hence, proved.
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