Verify that the statement is an identity 2Cscu 2Sinu 2 Cos

Verify that the statement is an identity 2Csc(u) - 2Sin(u) = 2 Cos(u Cot (u)

Solution

2csc(u)-2sin(u)

write csc(u)as 1/sin(u)

=(2/sin(u)) -2sin(u)

=(2-2sin²(u))/sin(u)

=2(1-sin²(u))/sin(u)

=2(cos²(u))/sin(u) ....................[since sin²(u)+cos²(u)=1]

=2cos(u)(cos(u)/sin(u))

=2cos(u)cot(u)