Question

log√1+cos(5x/2)/√1-cos(5x/2) differentiate​

Answer 1

Step-by-step explanation:

log√1+cos(5x/2)/√1-cos(5x/2 )

1+cos(5x/2)/√1-cos(5x/2) = (2cos^2(5x/2)/2) / 2sin^2(5x/2)/2

since 1+cosA=2cos^2( A/2),1-cosA=2sin^2 (A/2)

=cot^2(5x/4)

log√1+cos(5x/2)/√1-cos(5x/2 ) =log√cot^2(5x/4)

=logcot(5x/4)

differenciate with respect to x

d(log√1+cos(5x/2)/√1-cos(5x/2 ))/dx=d(logcot(5x/4))/dx

=1/cot(5x/4)dcot(5x/4)/dx

=1/cot(5x/4)(-cosec^2(5x/4))d(5x/4)/dx

= -(sin(5x/4) /cos(5x/4))(1/sin^2(5x/4)) *5/4

=-5/4(1/sin(5x/4)cos(5x/4))

=-5/(2sin(2*5x/4))

= -5/2sin5x/2