Obtain the solution that satisfies the given conditions of the differential equation, dy/dx = tanxtany , y = pi/4 at x = pi/4

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I am looking at this a bit at a time Alan.

$$\\\int{\frac{dy}{tan(y)}}\\\\ =\int{\frac{cos(y)}{sin(y)}}dy\\\\ =ln(sin(y))+k$$

Isn't that correct ?

Same thing Melody:

I might have got to the end result quicker if I'd used your formulation though!

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Thank Alan 

Also Melody, it's often advantageous to write the constant of integration as

$$\ln(k).$$

That allows the result to be written as

$$\ln(\sin y) + \ln(k) = \ln(k \sin y)$$

making later simplification easier.

Thanks Bertie   

That makes god sense  :)