If tan $\theta$ = $\frac{4}{3}$ then (sin $\theta$ + cos $\theta$) = ?

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KollegeApply · Accepted Answer

bb($\frac{7}{5}$) Explanation: tan $\theta$ = $\frac{4}{3}$ $\Rightarrow$ (BC)/(AB) = $\frac{4}{3}$ Let BC = 4k and AB = 3k. $\therefore$ AC2 = (AB2 + BC2) = (9k2 + 16k2) = 25k2 $\Rightarrow$ AC = sqrt(25k^2) $\Rightarrow$ AC = 5k $\therefore$ `(sin $\theta$ + cos $\theta$) = ((BC)/(AC) + (AB)/(AC)) = ((4k)/(5k) + (3k)/(5k)) = (7k)/(5k) = $\frac{7}{5}$` [Solution diagram: 470329_solution_1.png]

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