QUIZZZ
materi :Trigonometri
[tex]\rm Jika\\\\\displaystyle\sf\frac{\sin^4x}{2}+\frac{\cos^4x}{3}=\frac{1}{5}[/tex]
Tentukan nilai dari [tex]\sf\tan^2x=\cdots[/tex]
materi :Trigonometri
[tex]\rm Jika\\\\\displaystyle\sf\frac{\sin^4x}{2}+\frac{\cos^4x}{3}=\frac{1}{5}[/tex]
Tentukan nilai dari [tex]\sf\tan^2x=\cdots[/tex]
Verified answer
PEMBAHASAN
Trigonometri
sin² x + cos² x = 1
sin⁴ x/2 + cos⁴ x/3 = 1/5
kedua ruas kalikan 6
3 sin⁴ x + 2 cos⁴ x = 6/5
3 sin⁴ x + 2 (1 - sin² x)² = 6/5
3 sin⁴ x + 2 (1 - 2 sin² x + sin⁴ x) = 6/5
5 sin⁴ x - 4 sin² x + 2 = 6/5
25 sin⁴ x - 20 sin² x + 10 - 6 = 0
(5 sin² x - 2)² = 0
5 sin² x - 2 = 0
sin² x = 2/5
cos² x = 1 - sin² x = 3/5
tan² x
= sin² x / cos² x
= (2/5) / (3/5)
= 2/3