Question

if cot(x)+sin(x)=-cos(x)cot(x) then find the numerical value of cosx

Answer 1

\[\cot x+\sin x=-\cos x \cot x\]
\[\frac{ \cos x }{ \sin x }+\sin x=-\cos x*\frac{ \cos x }{ \sin x }\]
\[\frac{ \cos x+\sin ^{2}x+\cos ^{2} x }{ \sin x }=0\]
\[\cos x+1=0,\cos x=-1=\cos \left( \pi+2k \pi \right),x=\left( 2k+1 \right)\pi,where~k~is~an~integer.\]

Answer 2

cos x=-1