Question

вычислить tg^2 a, если известно, что  3 sin^2 a + 9 cos^2 a = 8

Answer 1

3 sin² a + 9 cos² a = 8

(3sin²α+3cos²α)+6cos²α=8

3(sin²α+cos²α)+6cos²α=8

3+6cos²α=8

6cos²α=8-3

6cos²α=5

cos²α=5-5cos²α

cos²α=5(1-cos²α)

cos²α=5sin²α

$tg^{2}alpha=frac{sin^{2}alpha}{cos^{2}alpha}=frac{sin^{2}alpha}{5sin^{2}alpha}=frac{1}{5}$

Answer 2

$3sin^2 a+9cos^2 a=8;\ 3sin^2 a+9cos^2 a=8*1;\ 3sin^2 a+9cos^2 a=8*(sin^2 a+cos^2 a);\ 3sin^2 a+9cos^2 a=8sin^2 a+8cos^2 a;\ 3sin^2 a-8sin^2 a=8cos^2 a-9cos^2 a;\ -5sin^2 a=-cos^2 a;\ 5sin^2 a=cos^2 a;\ tg^2 a=frac{1}{5}=0.2$