If y = ∑ (k=1,6)k cos-1 {3/5coskx - 4/5sinkx} then dy/dx at x = 0 is ......

Question

If y = \(\displaystyle\sum_{k=1}^{6} \) k cos^-1 {3/5coskx - 4/5sinkx} then dy/dx at x = 0 is ......

Answer 1

Put cosα = 3/5,sinα = 4/5 0<α< π/2

Now 3/5 coskx - 4/5sinkx

= cosα . cos kx – sinα . sin kx

= cos(α + kx)

As we have to find derivate at x = 0

We have cos^–1 (cos(α + kx))

= (α + kx)