If cos x 45 csc x Solutiongiven cosx45 cscx1sinxsinx x is i

Solution

given cosx=4/5

cscx<0 =>1/sinx<0 =>sinx <0

=> x is in 4th quadrant

adjacent side =4 , hypotenuse =5

oppositeside²+adjacent side² = hypotenuse²

oppositeside²+4² = 5²

oppositeside² = 9

opposite side =3

sinx =oppositeside/hypotenuse

sinx=-3/5

sin2x =2sinxcosx

sin2x=2*(-3/5)(4/5)

sin2x=-24/25

cos2x =cos²x-sin²x

cos2x=(4/5)²-(-3/5)²

cos2x=(16/25)-(9/25)

cos2x=(7/25)

tan2x= sin2x/cos2x

tan2x=(-24/25)/(7/25)

tan2x =-24/7