If 4 tan $\theta$ = 3 then (cos2$\theta$ – sin2$\theta$) = ?

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KollegeApply · Accepted Answer

bb($\frac{7}{25}$) Explanation: tan $\theta$ = $\frac{3}{4}$ $\Rightarrow$ (BC)/(AB) = $\frac{3}{4}$ Let BC = 3k. Then, AB = 4k. In right ΔABC, we have AC2 = AB2 + BC2 = (4k)2 + (3k)2 = 25k2 $\Rightarrow$ AC = sqrt(25k^2) $\Rightarrow$ AC = 5k $\therefore$ `(cos^2$\theta$ - sin^2$\theta$) = ((AB)/(AC))^2 - ((BC)/(AC))^2 = ((4k)/(5k))^2 - ((3k)/(5k))^2 = ($\frac{16}{25}$ - $\frac{9}{25}$) = $\frac{7}{25}$` [Solution diagram: 470339_solution_1.png]

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