Answer:
Option A.
Step-by-step explanation:
It is given secθ = - [tex]\frac{4}{3}[/tex]
then cosθ = -[tex]\frac{3}{4}[/tex]
Now we know the identity
sinθ = [tex]\sqrt{1-cos^{2}\theta }[/tex]
= [tex]\sqrt{1-(-\frac{3}{4} )^{2}}[/tex]
= [tex]\frac{\sqrt{7} }{4}[/tex]
Now sin2θ = 2sinθcosθ
Now we put the values of cosine and sine in the formula
sin2θ = 2×(-[tex]\frac{3}{4}[/tex])([tex]\frac{\sqrt{7}}{4}[/tex])
= -[tex]\frac{3\sqrt{7}}{8}[/tex]
Therefore, option A. is the answer.
