Question

Find value of theta

Sin(40+theta)cos(10+theta)-cos(40+theta)sin(10+theta)=1/2

Answer 1

Hey there !!!!!

sin(40+θ)cos(10+θ)-cos(40+θ)sin(10+θ)=

given is of the form

sinAcosB-cosAsinB=sin(A-B)

here A=40+θ, B=10+θ

So sin(40+θ-10-θ)------Equation 1

    =sin30=1/2

   LHS=RHS
 
and from equation 1 we can observe that θ can take any value(there exists infinite values of θ )

Hope this helped you.....................

Answer 2

Hi friend!!!!

Given, sin(40+∅)cos(10+∅)-cos(40+∅)sin(10+∅)

(It is in the form of sinAcosB -sinB cosA=sin(A-B))

→sin(40+∅-10-∅)

=sin30

=1/2

L.H.S =R.H.S


hence proved

I hope this will help u ;)