Question

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

Answer 1

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 ((180+x+x)/(2) ) ~cos ((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.`

`(tan (5\pi )/(3)-tan (\pi )/(6) )/(1+tan (5\pi )/(3) tan(\pi )/(6) ) \\=tan ((5\pi )/(3) -(\pi )/(6) )\\=tan((9\pi )/(6) \\=tan ((3\pi )/(2) )\\`

→-∞

Answer 2

Explanation:

cos(180˚)cos(x)−sin(180˚)sinx=−cosx

−1(cosx)−0(sinx)=−cosx

−cosx=−cosx