1. Buktikan bahwa: sec A + tan A = cos A / 1-sin A 2. Buktikan bahwa tan 75+tan15=4 Tolong jawab ya

Trigonometry.

Number 1.
a - b = (a - b)(a + b) / (a + b) = (a² - b²) / (a + b)

cos A / (1 - sin A)
= cos A / [(1 - sin² A) / (1 + sin A)]
= cos A / [cos² A / (1 + sin A)]
= (1 + sin A) / cos A
= 1 / cos A + sin A / cos A
= sec A + tan A
Proved.

Number 2.
[tex]\displaystyle \boxed{\sin (\alpha +\beta )=\sin \alpha \cos \beta +\cos \alpha \sin \beta}\\ \boxed{\cos \alpha \cos \beta =\frac{1}{2}[\cos (\alpha +\beta )+\cos (\alpha -\beta )]}[/tex]

[tex]\displaystyle \tan 75^{\circ}+\tan 15^{\circ}\\ =\frac{\sin 75^{\circ}}{\cos 75^{\circ}}+\frac{\sin 15^{\circ}}{\cos 15^{\circ}}\\ =\frac{\sin 75^{\circ}\cos 15^{\circ}+\cos 75^{\circ}\sin 15^{\circ}}{\cos 75^{\circ}\cos 15^{\circ}}\\ =\frac{\sin (75^{\circ}+15^{\circ})}{\frac{1}{2}[\cos(75^{\circ}+15^{\circ})+\cos(75^{\circ}-15^{\circ})]}\\ =\frac{1}{\frac{1}{2}(0+\frac{1}{2})}\\ =4[/tex]