Simplify-cos-1-sin-x-cos-x-2-pi-4-lt-x-lt-5pi-4-

Question Number 20506 by Tinkutara last updated on 27/Aug/17

S i m p l i f y :

\cos^{- 1} (\frac{\sin x + \cos x}{\sqrt{2}}), \frac{π}{4} < x < \frac{5 π}{4}

Answered by ajfour last updated on 27/Aug/17

θ = \cos^{- 1} [\cos (π / 4) \cos x + \sin (π / 4) \sin x]

= \cos^{- 1} [\cos (x - π / 4)]

A n d a s π / 4 < x < 5 π / 4

s o 0 < x - π / 4 < π

H e n c e θ = x - π / 4 .

Commented by Tinkutara last updated on 27/Aug/17

Thank you very much Sir!