Question

Rezolvati ecuatiile :
a) sin(arcsin 2/3 + arcsin 1/4)
b) cos(arcsin(-1/4)+arcsin 1/50
c)sin(2arcsin rad3/2)

Answer 1

Explicație pas cu pas:

$\sin( \arcsin( \frac{2}{3} ) + \arcsin( \frac{1}{4} )) = \sin(\arcsin( \frac{2}{3})) \times \cos(\arcsin( \frac{1}{4})) + \cos(\arcsin( \frac{2}{3})) \times \sin(\arcsin( \frac{1}{4} ))= \frac{2}{3} \times \sqrt{1 - (\frac{1}{4})^{2} } + \frac{1}{4} \times \sqrt{1 - (\frac{2}{3})^{2}}= \frac{ \sqrt{15} }{6} + \frac{ \sqrt{5} }{12} =\frac{\sqrt{5}(2 \sqrt{3} + 1)}{12}$

$\cos( \arcsin( \frac{ - 1}{4} ) + \arcsin( \frac{1}{50} ))$