Question

2 sin^2 π/6 +cosec 7π/6 cos ^π/6

Answer 1

sin(pi/6)=1/2

sin^2(pi/6)=1/4

2sin^2(pi/6)=2/4=1/2

Then: cosec(7pi/6)=-2

So: cosec^2(7pi/6)=(-2)^2=4

And cos(pi/3)=sqrt(3)/2

So cos^2(pi/3)=3/4

And so: 2sin^2(pi/6)+cosec^2(7pi/6)cos^2(pi/3)= 1/4 + 4*3/4=1/4 + 3 =13/4