Sederhanakan tan(x+45)
Matematika
Silminaunyil
Pertanyaan
Sederhanakan tan(x+45)
1 Jawaban
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1. Jawaban RexyGamaliel
tan (x+45°)
= [tex] \frac{sin (x+45)}{cos (x+45)} [/tex]
= [tex] \frac{sin x . cos 45 + sin 45 . cos x}{cos x . cos 45 - sin x . sin 45} [/tex]
= [tex] \frac{\frac{\sqrt{2}}{2} . sin x + \frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2} . cos x - \frac{\sqrt{2}}{2} . sin x} [/tex]
= [tex] \frac{\sqrt{2}}{2} . \frac{cos x + sin x}{cos x - sin x} [/tex]
= [tex] \frac{\sqrt{2}}{2} . \frac{cos x + sin x}{cos x - sin x} . \frac{cos x - sin x}{cos x - sin x} [/tex]
= [tex] \frac{\sqrt{2}}{2} . \frac{cos^2 x - sin^2 x}{cos^2 x + sin^2 x - 2 . sin x . cos} [/tex]
= [tex] \frac{\sqrt{2}}{2} . \frac{cos (2x)}{1 + sin (2x)} [/tex]