Question

Cos(180 +x)=-cos(x) use sum and difference Formula​

Answer 1

Step-by-step explanation:

cos(180˚)cos(x)−sin(180˚)sinx=−cosx

−1(cosx)−0(sinx)=−cosx

−cosx=−cosx

Answer 2

Answer:

Step-by-step explanation:

cos (180+x)=-cos x

cos (180+x)=cos 180cos x-sin 180 sin x

=(-1)cos x-0 (sin x)

=-cos x-0

=-cos x

so cos(180+x)=-cos x

if you want to find x then

cos (180+x)+cos x=0

$2 cos (\frac{180+x+x}{2} ) ~cos (\frac{180+x-x}{2} )=0\\or~\\cos (90+x) cos 90=0\\which~ is~ true~ for~ all~ x ~as~cos~90=0\\x=all~real~numbers.$

$\frac{tan \frac{5\pi }{3}-tan \frac{\pi }{6} }{1+tan \frac{5\pi }{3} tan\frac{\pi }{6} } \\=tan (\frac{5\pi }{3} -\frac{\pi }{6} )\\=tan(\frac{9\pi }{6} \\=tan (\frac{3\pi }{2} )$

→-∞