Please help? trigonometry

Question

392 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-01T18:20:24

The correct answer is #"option b"#

We need

#costheta=1-2sin^2(theta/2)#

#sin^2theta+cos^2theta=1#

#costheta=8/17#

Therefore,

#2sin^2(theta/2)=1-costheta=1-8/17=9/17#

#sin^2(theta/2)=1/2*9/17=9/34#

#sin(theta/2)=sqrt(9/34)=3/sqrt(34)=(3sqrt(34))/34#

#sin(2theta)=2sinthetacostheta#

#=2*sqrt(1-(8/17)^2)*8/17#

#=2sqrt(1-64/289)*8/17#

#=2*sqrt(225/289)*8/17#

#=2*15/17*8/17#

#=240/289#

The correct answer is #"optionb"#