Question

If `sin(picostheta)=cos(pi sintheta),t h e n sin2theta=`

Answer 1

`sin(picostheta) = cos(pisintheta)`
`=>cos(pi/2-picostheta) = cos(pisintheta)`
`=>pi/2-picostheta = +-pisintheta`
`=>1/2 = sintheta+-costheta`
`=>(1/2)^2 = (sintheta+-costheta)^2`
`=>1/4 = sin^2theta+cos^2theta+-2sinthetacos theta`
`1/4 = 1+-sin2theta`
`=>+-sin2theta = 1/4-1 = -3/4`
`:. sin2theta = +-3/4.`