If csc x 5 and cos x 0 find sin2xSolutioncscx5 sinx15 henc

If csc x = -5 and cos x > 0, find sin(2x).

Solution

cscx=-5

-->sinx=-1/5

hence perpendicular=-1,hypotenuese=5 (because cosx>0)

by pythagoreus theroem

h^2=p^2+b^2

5^2=-1^2+b^2

25-1=b^2

b=2sqrt(6)

hence cosx=2sqrt(6)/5

now sin(2x)=2sinxcosx

=2(-1/5)(2sqrt(6)/5)

=-4sqrt(6)/25