Question

Buktikan bahwa [tex]\frac{1 + \tan {A}}{ \sin {A} + \cos {A}} = \sec {A} [/tex]

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Answer 1

Verified answer

Penjelasan dengan langkah-langkah:

Pembuktian Identitas trigonometri

[tex]\begin{aligned}\rm\frac{1+\tan A}{\sin A+\cos A}&=\sec A \\\rm \frac{1 + \frac{ \sin A }{\cos A} }{\sin A+\cos A} &= \sec A\\\rm \frac{\frac{\cos A+\sin A}{\cos A}}{\sin A+\cos A}&= \sec A\\\rm\frac{\cancel{\cos A+\sin A}}{\cos A}\times\frac{1}{\cancel{\sin A+\cos A}}&=\sec A\\\rm\frac{1}{\cos A}&=\sec A\\&\because\boxed{\sec X=\frac{1}{\cos X}}\\ \\ \rm\therefore \sec A&=\sec A\cdots\left[Terbukti\:\:✓\right]\end{aligned}[/tex]