# If tanθ = 4/3, show that sinθ + cosθ = 7/5

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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