Question

sin120°cos150°+cos120°sin150° is equal to​

Answer 1

To Find:

Value of sin120°cos150°+cos120°sin150°

Solution:

We know that,

➳ sin(A+B)= sinAcosB+cosAsinB

➳ sin(270°)= -1

Now,

$\mathrm{sin120^{\circ}cos150^{\circ}+cos120^{\circ}sin150^{\circ}=sin(120^{\circ}+150^{\circ})}$

$\mathrm{sin120^{\circ}cos150^{\circ}+cos120^{\circ}sin150^{\circ}=sin(270^{\circ})}$

$\mathrm{\pink{sin120^{\circ}cos150^{\circ}+cos120^{\circ}sin150^{\circ}=-1}}$

Hence, the required value of is -1.

$\rule{190}{2}$

Few more Identities

➳ sin(A-B)= sinAcosB-cosAsinB

➳ cos(A+B)= cosAcosB-sinAsinB

➳ cos(A-B)= cosAcosB+sinAsinB