If tan $\theta$ = $\frac{12}{5}$, then 5 sin $\theta$ – 12 cos $\theta$ = ?

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KollegeApply · Accepted Answer

0 Explanation: Here, tan $\theta$ = $\frac{12}{5}$ Now, according to Pythagoras theorem, AC2 = AB2 + BC2 AC2 = 122 + 52 $\Rightarrow$ AC2 = 144 + 25 $\Rightarrow$ AC2 = 169 $\Rightarrow$ AC = 13 Hence, sin $\theta$ = (AB)/(AC) = $\frac{12}{13}$ And cos $\theta$ = (BC)/(AC) = $\frac{5}{13}$ So, 5 sin $\theta$ – 12 cos $\theta$ = 5 xx $\frac{12}{13}$ - 12 xx $\frac{5}{13}$ = $\frac{60}{13}$ - $\frac{60}{13}$ = 0

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