Question

SA se calculeze. sin(arcsin1/2+arccos1/2)

Answer 1

sinarcsin X=X , sinarccosX= $\sqrt{1- cos^{2}arccosX }= \sqrt{1-( cosarccosX)^{2} } = \sqrt{1- X^{2} }$.
La fel se obtine cosarcsinX=$\sqrt{1- x^{2} }$
Stim ca sin(A+B)= sinA.cosB+sinB.cosA, deci :

expresia data = sinsrcsin 1/2*cosarccos 1/2 +sinarccos 1/2*cosarccos 1/2=

1/2$\sqrt{1- \frac{1}{4}$+1/2$\sqrt{1- \frac{1}{4} }$=2*(1/2)$\sqrt{ \frac{3}{4} }$=$\frac{ \sqrt{3} }{2}$