$If A+B+C=180° then match the following$

 

List-I	List-II
cosA+cosB+cosC	2+2cosAcosBcosC
sin2A+sin2B+sin2C	4cosA/2cosB/2cosC/2
sin2A+sin2B+sin2C	1+4sinA/2sinB/2sinC/2
sinA+sinB+sinC	4sinAsinBsinC

 

 

If A + B + C = ${180}^0$ then $\sin 2\mathrm{A}+\sin 2\mathrm{B}+\sin 2\mathrm{C}=4\mathrm{sinA} \mathrm{sinB} \mathrm{sinC}$

If A + B + C = ${180}^0$ then $\cos A + \cos B + \cos C$$=1+ 4\sin \frac{\mathrm{A}}{2} \sin \frac{\mathrm{B}}{2} \sin \frac{\mathrm{C}}{2}$

If A + B + C = ${180}^0$ then ${\sin }^2\mathrm{A} + {\sin }^2\mathrm{B} + {\sin }^2\mathrm{C}$$=2+ 2\mathrm{cosA} \mathrm{cosB} \mathrm{cosC}$

If A + B + C = ${180}^0$ then $\sin A + \sin B + \sin C$$=4\cos \frac{\mathrm{A}}{2} \cos \frac{\mathrm{B}}{2} \cos \frac{\mathrm{C}}{2}$

(The above results can be verified by assuming A=B=C=60 degrees)

$1-c,2-a,3-d,4-b$