Sunday

January 22, 2017
Posted by **marley** on Wednesday, June 8, 2011 at 11:52am.

- maths (trigonometry) -
**Reiny**, Wednesday, June 8, 2011 at 12:36pm√2sinx + sinx = cosx

sinx(√2+1)= cosx

sinx/cosx = 1/(√2+1)

tanx = 1/(√2+1)

now construct a right-angled triange with sides 1 and √2+1

let the hypotenuse be r

r^2 = 1^2 + (√2+1)^2 = 1 + 2 + 2√2 + 1 = 4 + 2√2

r = √(4+2√2))

cosx + sinx = (√2+1)√(4+2√2) + 1/(√(4+2√2)

= (√2 + 2)/(√(4 + 2√2)

You might want to rationalize this to get a different looking answer.