If $3 tan x = 4$ , then find the value of $5 (sin x + cos x)$ .

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Solution

$G i v e n$ $t a n x = (\frac{4}{3}) ∴ s i n x = (\frac{4}{\sqrt{4^{2} + 3^{2}}}) = (\frac{4}{5}) ∴ c o s x = (\frac{3}{5}) s o 5 (s i n x + c o s x) = 5 ((\frac{4}{5}) + (\frac{3}{5})) = 7$

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