Question

Mohon bantuannya,, tolong jangan asal jawab,,

Answer 1

Verified answer

TriGonoMetRi

(cos² x - sin² x)/(sin x cos x) = a
cos 2x / (1/2 sin 2x) = a
cot 2x = a/2
tan 2x = 1/cot 2x = y/x = 2/a

r = √(2² + a²) = √(4 + a²)
sin 2x = y/r = 2/√(4 + a²)
sin² 2x = 4/(4 + a²)

•••
cot² x + tan² x
= (csc² x - 1) + (sec² x - 1)
= (cos² x + sin² x)/(sin x cos x)² - 2
= 1/(1/2 sin 2x)² - 2
= 4/(4/(4 + a²)) - 2
= (4 + a²) - 2
= 2 + a² ✔