Tolong buktikan identitas trigonometri berikut; tan^{2}x +sin^{2}x = (sec x +cos x) (sec x

September 2018 2 93 Report

Tolong buktikan identitas trigonometri berikut;
tan^{2}x +sin^{2}x = (sec x +cos x) (sec x - cos x)

Aremon Tan^2(x) + sin^2(x) = $\frac{sin ^{2}x }{cos ^{2}x } + \frac{sin ^{2}x }{cos ^{2}x } cos ^{2}x$
= $\frac{sin ^{2}x(1+cos ^{2} x) }{cos ^{2} x}$
= $\frac{(1-cos ^{2} x)(1+cos ^{2} x)}{cos ^{2} x}$
= $\frac{1-cos ^{4} x}{cos ^{2} x}$
= $\frac{1}{cos ^{2} x} -cos ^{2} x$
= $sec ^{2} x-cos ^{2} x$
=(sec x + cos x)(sec x - cos x)

3 votes Thanks 1

hendrisyafa $tan^{2}x$ + $sin^{2} x$ = (sec x+cos x) (sec x - cos x)
olah pada ruas kiri
$\frac{ sin^{2}x }{ cos^{2} x}$ + $\frac{ sin^{2}x }{1}$
samakan penyebut
$\frac{ sin^{2}x + sin^{2}x . cos^{2}x }{ cos^{2}x } = \frac{ sin^{2}x (1+ cos^{2}x) }{ cos^{2}x }$
= $\frac{ (1- cos^{2} x) (1+ cos^{2}x )}{ cos^{2}x } = \frac{1- cos^{4}x }{ cos^{2}x }$
= $\frac{1}{ cos^{2}x} - \frac{ cos^{4}x }{ cos^{2}x } = sec^{2}x - cos^{2}x$
= (sec x + cos x) (sec x - cos x)

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