Question

Sendo sex x=√3/2 determine:
A)seno +cosseno
B)seno +tg
C)seno+cosseno+secante
D)seno-cosseno+cosseno

Answer 1

$Sen^{2} X+Cos ^{2} X= 1$
$( \frac{ \sqrt{3} }{2} )^{2} + cos ^{2} X= 1$
$\frac{3}{4}+ cos^{2} X=1$
$cos^{2} X= \frac{1}{4}$
$cos X= \frac{1}{2}$
$X= 60$

a)sen + cos= $\frac{1}{2} + \frac{ \sqrt{3} }{2} = \frac{1+ \sqrt{3} }{2}$

b)sen + tg=$\frac{ \sqrt{3} }{2} + \sqrt{3}= \frac{3 \sqrt{3} }{2}$

c)sen + cos + sec= $\frac{1}{2}+ \frac{ \sqrt{3} }{2} + \frac{1}{cosX}$
$\frac{ 1+\sqrt{3} }{2} + \frac{2}{ \sqrt{3} } = \frac{ \sqrt{3}+3+4} {2 \sqrt{3} } = \frac{3+7 \sqrt{3} }{6}$

d)sen - cos + cos= sen= $\frac{ \sqrt{3} }{2}$