My doubt lies with the following question. It is given that sin(pi*cosx) = cos(pi*sinx). From the following information it is to be proved that x = (1/4)[(2n+1)pi +or- cos^-1(1/8)] where n is any natural number. From the question we can make it clear that the range of pi*cosx and pi*sinx is between pi and -pi. So I took two cases. In the first case bot are positive. When they are positive they must lie in [0,pi/2]. Thus from the equation we get that pi*cosx and pi*sinx must be complementary. Therefore pi*cosx = pi/2 - pi*sinx. Therefore cosx = (1/2) - sinx. Therefore sinx + cosx = (1/2) and this is the maxima of the function thus bringing up that x is 2n*pi + pi/4 in case1 while it is 2n*pi -3pi/4 in case2. So that is something that is against my question or infact I have disproved what I should prove. Can anyone help?