Question

Given sec theta=-4/3 and 90°

Answer 1

Option A.

Explanation:

It is given secθ = -
`(4)/(3)`

then cosθ = -
`(3)/(4)`

Now we know the identity

sinθ =
`\sqrt{1-cos^(2)\theta }`

=
`\sqrt{1-(-(3)/(4) )^(2)}`

=
`(√(7) )/(4)`

Now sin2θ = 2sinθcosθ

Now we put the values of cosine and sine in the formula

sin2θ = 2×(-
`(3)/(4)`)(
`(√(7))/(4)`)

= -
`(3√(7))/(8)`

Therefore, option A. is the answer.