Jika tan x = 1/2, maka nilai dari 2 sin x + sin (x + [tex] \pi [/tex]/2) + cos([tex] \pi [/tex] - x)...
Matematika
Azolla11
Pertanyaan
Jika tan x = 1/2, maka nilai dari 2 sin x + sin (x + [tex] \pi [/tex]/2) + cos([tex] \pi [/tex] - x)...
1 Jawaban
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1. Jawaban whongaliem
tan x = 1/2
tan² x + 1 = 1/cos² x
(1/2)² + 1 = 1/cos² x
1/4 + 1 = 1/cos² x
5/4 = 1/cos² x
cos² x = 4/5
cos x = √(4/5)
cos x = (2/5)√5
sin x = tan x . cos x
= (1/2) .(2/5)√5
= (1/5)√5
2.sin x + sin (x +π/2) + cos (π - x) = 2.sin x + cos x - cos x
= 2.sin x
= 2 (1/5)√5
= (2/5)√5