My doubt lies with the following question. It is given that sin(pi*cosx) = cos(pi*sinx).(adsbygoogle = window.adsbygoogle || []).push({});

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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Trigo doubt

**Physics Forums | Science Articles, Homework Help, Discussion**