Question

Prove that Cos165°+Sin165°=Cos135°

Answer 1

Step-by-step explanation:

we know that ,

#color(red)((1)sin(x+y)=sinxcosy+cosxsiny#

Here ,

#sin165^circ=color(red)(sin(135^circ+30^circ)tocolor(red)(Apply(1)#

#sin165^circ=color(red)(sin135^circcos30^circ+cos135^circsin30^circ#

#sin165^circ=1/sqrt2*sqrt3/2+(-1/sqrt2)*1/2#

#sin165^circ=1/sqrt2*sqrt3/2-1/sqrt2*1/2#

#sin165^circ=(sqrt3-1)/(2sqrt2)#

#sin165^circ=(sqrt3-1)/(2sqrt2)xxsqrt2/sqrt2#

#sin165^circ=(sqrt6-sqrt2)/4#