Cos¯¹ (1/5) [ 3 Cos x - 4 Sin x ] = y (say)
=> Cos y = (1/5) [ 3 Cos x - 4 Sin x ]
=> ...= (3/5) Cos x - (4/5) Sin x
angle of ' A ' such that Cos A = 3/5 and Sin A = 4/5
both Sin A and Cos A are constant quantities .
=>..= Cos A. Cos x - Sin A. Sin x
Using formula Cos A . Cos B - Sin A. Sin B = Cos ( A + B ) we get
=> Cos y = Cos ( A + x )
Hence y = A + x
Differentiating both the sides w.r.t x , taking care that ' A ' is a constant we get
=> y' = 0 + 1
dy/dx = 1