Q. 184.2( 11 Votes )

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

Answer :

We have, tanθ = (4k)/(3k) = BC/AC (For some value of k)

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

∴AB^{2} = BC^{2} + AC^{2}

= AB^{2} = (4k)^{2} + (3k)^{2}

= AB^{2} = 16k^{2} + 9k^{2}

= AB^{2} = 25k^{2}

= (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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