Find-sin-2x-pi-4-

Question Number 208075 by hardmath last updated on 04/Jun/24

Find : \int \sin (2 x - \frac{π}{4}) = ?

Answered by TonyCWX08 last updated on 04/Jun/24

s i n (2 x - \frac{π}{4})

= s i n (2 x) c o s (\frac{π}{4}) - s i n (\frac{π}{4}) c o s (2 x)

= \frac{\sqrt{2}}{2} (s i n (2 x) - c o s (2 x))

\frac{\sqrt{2}}{2} \int s i n (2 x) - c o s (2 x) d x

= \frac{\sqrt{2}}{2} (- \frac{c o s (2 x) + s i n (2 x)}{2}) + c

= - \frac{\sqrt{2} (c o s (x) + s i n (x))}{4} + c