Question

Пожалуйста помогите!!!❤❤❤❤

Answer 1

а) sin2×75°=sin150°=1/2
б)
$\sin(2 \times \frac{\pi}{8} ) = \sin( \frac{\pi}{4} ) = \frac{ \sqrt{2} }{2}$
в)
$\frac{1}{2} \sin(2 \times {15}^{0} ) = \frac{1}{2} \sin( {30}^{0} ) = \\ = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$
${ \cos }^{2} \frac{\pi}{8} + 2 \cos( \frac{\pi}{8} ) \times \sin( \frac{\pi}{8} ) + \\ + { \sin}^{2} \frac{\pi}{8} = \sin(2 \times \frac{\pi}{8} ) + 1= \\ = \sin( \frac{\pi}{4} ) + 1 = \frac{ \sqrt{2} }{2} + 1$
д)

${ \sin}^{2} \frac{\pi}{12} - 2 \sin( \frac{\pi}{12} ) \times \cos( \frac{\pi}{12} ) + \\ + { \cos}^{2} \frac{\pi}{12} = 1\ - sin(2 \times \frac{\pi}{12} ) = \\ = 1 - \sin( \frac{\pi}{6} ) = 1 - \frac{1}{2} = \frac{1}{2}$
е)
$\cos(2 \times {75}^{0} ) = \cos( {150}^{0} ) = \frac{1}{2}$
ж)

$\cos( 2 \times \frac{\pi}{8} ) = \cos( \frac{\pi}{4} ) = \frac{ \sqrt{2} }{2}$
з)
$- \cos(2 \times \frac{\pi}{12} ) = - \cos( \frac{\pi}{6} ) = - \frac{ \sqrt{3} }{2}$

Answer 2

a)sin2*75=sin150=1/2

b)sin π/4 = √2/2

c) 1/2 sin30 = 1/2 * 1/2=1/4 

d)cos² π/8+sin² π/8 +2sin π/8cosπ/8 = 1+sinπ/4 = 1+ √2/2

e)sin² π/12 +cos²π/12 -2sin π/12cosπ/12= 1-sin π/6 = 1-1/2=1/2

f)cos2*75 = cos 150=1/2

g)cos π/4 = √2/2

h)1-cos² π/12 - cos² π/12 = sin² π/12 - cos ² π/12 = -cos π/6= -√3/2