Answer :
We have, tanθ = (4k)/(3k) = BC/AC (For some value of k)
By Pythagoras theorem, (hypotenuse)2 = (perpendicular)2 + (base)2
∴AB2 = BC2 + AC2
= AB2 = (4k)2 + (3k)2
= AB2 = 16k2 + 9k2
= AB2 = 25k2
= (5k)2
→ AB = 5k
sinθ = BC/AB = (4k)/(5k) = 4/5
cosθ = AC/AB = (3k)/(5k) = 3/5
consider LHS = sinθ + cosθ = 
= 7/5
= RHS
HENCE PROVED
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NCERT - Mathematics