Question

Найти cos 2α, если tg α = 3/4
π<α<3π/2

Answer 1

$tgalpha=frac34\1+tg^2alpha=frac1{cos^2alpha}\cos^2alpha=frac1{1+tg^2alpha}\cosalpha=pmsqrt{frac1{1+tg^2alpha}}=pmsqrt{frac1{1+frac9{16}}}=pmsqrt{frac1{frac{25}{16}}}=pmsqrt{frac{16}{25}}=pmfrac45\pi textless alpha textless frac{3pi}2Rightarrow cosalpha textless 0\cosalpha=-frac45\cos2alpha=2cos^2alpha-1=2cdotfrac{16}{25}-1=frac{32}{25}-1=frac7{25}$