dla pewnego kata 0°<α<90° prawdziwy jesr wzor tgα+1/tgα=3cos⁻¹α.oblicz wartosci funkcji trygometrycznych kata α.

tgα + (1/tgα) = 3/cos α , dla 0⁰ < α < 90⁰ sinα/cosα + cosα / sinα = 3 /cosα [sin²α + cos²α]/[sinα cosα] = 3 /cosα 1/[sinα cos α] = 3/ cosα cosα = 3 sinα cosα 3 sin α = 1 sin α = 1/3 cos²α = 1 - sin²α = 1 -(1/3)² = 9/9 - 1/9 = 8/9 cos α = √8/√9 = 2√2 /3 tg α = sinα / cosα = (1/3) /(2√2 /3) = (1/3)*(3/2√2) = 1/2√2 =√2/4 ctg α = 1 /tgα = 1/(√2/4) = 4/√2 = 2√2