How do you solve $cos x + 1 = sin x$ $cosx+1=sinx$ ?

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How do you solve $cos x + 1 = sin x$ $cosx+1=sinx$ ?

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Answer 1 · 2015-08-20T12:57:03

$x = n π + ({(- 1)}^{n} + 1) \frac{π}{4}$ $x = npi + ((-1)^n+1)pi/4$

Explanation:

$sin x - cos x = 1$ $sin x - cos x = 1$
$\sqrt{2} (\frac{1}{\sqrt{2}} sin x - \frac{1}{\sqrt{2}} cos x) = 1$ $sqrt(2)(1/sqrt(2) sin x - 1/sqrt(2) cos x)= 1$
$\sqrt{2} sin (x - \frac{π}{4}) = 1$ $sqrt(2)sin (x-pi/4) = 1$
$sin (x - \frac{π}{4}) = \frac{1}{\sqrt{2}}$ $sin (x-pi/4) = 1/sqrt(2)$

General solution:
$x - \frac{π}{4} = n π + {(- 1)}^{n} \frac{π}{4}$ $x - pi/4 = npi + (-1)^npi/4$
$x = n π + ({(- 1)}^{n} + 1) \frac{π}{4}$ $x = npi + ((-1)^n+1)pi/4$

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How do you solve $cos x + 1 = sin x$ $cosx+1=sinx$ ?

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How do you solve $cos x + 1 = sin x$ $cosx+1=sinx$ ?