Question

sec θ =5 , find sin (2θ)

Answer 1

sin2x=2(sinx)(cosx)
secx=5
1/cosx =5
cosx=1/5

x can be in quadrant 1 or 4 for cosx is +ve
for quadrant 1, both sin and cos is +ve
sinx=(sqrt24)/5
cosx=1/5
sin2x=2sinxcosx=2((sqrt24)/5)(1/5)
for quadrant 4,
sinx is -ve.
sin2x=2(sinx)(cosx)=2(-(sqrt24)/5)(1/5)