tozsamosc trygometryczna

[paulinka18]

oblicz:
a) 4 cos60' - sin30' - cos30' - sin60'
b) (tg60' - sin30') * ( cos60;' - ctg60')

Uzasadnij tozsamosc:
c) \(\displaystyle{ cos}\)\(\displaystyle{ \alpha}\) + \(\displaystyle{ cos^{2}}\) \(\displaystyle{ \alpha}\) = \(\displaystyle{ \frac{ctg\alpha}{sin\alpha}}\)

d) \(\displaystyle{ cos\alpha}\) * \(\displaystyle{ \frac{tg\alpha}{sin\alpha}}\) = \(\displaystyle{ 1}\)

[matshadow]

d)
\(\displaystyle{ \cos\alpha\frac{\frac{\sin\alpha}{\cos\alpha}}{\sin\alpha}=\cos\alpha\frac{1}{\cos\alpha}=1}\)

[gelo21]

Witam
a)
4 cos60' - sin30' - cos30' - sin60'=\(\displaystyle{ 4*1/2-1/2- \sqrt{3}/2-\sqrt{3}/2= \frac{3- \sqrt{3} }{2}}\)
b)
(tg60' - sin30') * ( cos60;' - ctg60')=\(\displaystyle{ ( \sqrt{3}- \frac{1}{2} )*( \frac{1}{2}- \frac{ \sqrt{3} }{3})}\)=\(\displaystyle{ \frac{(2 \sqrt{3}-1)(3-2 \sqrt{3} }{12}= \frac{8 \sqrt{3}-15 }{12}}\)

d) cos \alpha * \frac{tg \alpha}{sin \alpha} = 1
L=\(\displaystyle{ cosx* \frac{ \frac{sinx}{cosx} }{sinx}=cosx* \frac{sinx}{cosx}* \frac{1}{sinx}=1=P}\)