Solve-for-real-numbers-3-sin-2x-4sin-x-pi-4-

Question Number 156482 by MathSh last updated on 11/Oct/21

Solve for real numbers :

3 + \sin (2 x) = 4 \sin (x + \frac{π}{4})

Answered by mr W last updated on 11/Oct/21

3 + \sin (2 x) = 2 \sqrt{2} (\sin x + \cos x)

9 + 6 \sin (2 x) + \sin^{2} (2 x) = 8 (1 + \sin (2 x))

\sin^{2} (2 x) - 2 \sin (2 x) + 1 = 0

\Rightarrow \sin (2 x) = 1 \dots (i)

3 + 1 = 4 \sin (x + \frac{π}{4})

\Rightarrow \sin (x + \frac{π}{4}) = 1 . . (i i)

x + \frac{π}{4} = 2 k π + \frac{π}{2}

\Rightarrow x = 2 k π + \frac{π}{4}

i t f u l f i l l s b o t h (i) a n d (i i) .

Commented by MathSh last updated on 11/Oct/21

Very nice solution dear S er, thank you

Facebook Tweet Pin