Question

Question #50f3b

Answer 1

`sin2x=(4sqrt21)/25`

Explanation:

`"using the "color(blue)"trigonometric identities"`

`•color(white)(x)sin2x=2sinxcosx`

`•color(white)(x)sin^2x+cos^2x=1`

`rArrcosx=+-sqrt(1-sin^2x)`

`"x is in the third quadrant where "cosx<0`

`rArrcosx=-sqrt(1-(-2/5)^2)`

`color(white)(rArrcosx)=-sqrt(21/25)=-sqrt21/5`

`rArrsin2x=2xx-2/5xx-sqrt21/5=(4sqrt21)/25`