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Maths-

General

Easy

Question

The general solution of the trigonometric equation $sin invisible function application x plus cos invisible function application x equals 1$ is given by

$x = 2 n π, n = 0, \pm 1, \pm 2, \dots$
$x = 2 n π + π / 2; n = 0, \pm, \pm 2, \dots$
$x = n π + {(- 1)}^{n} \frac{π}{4} - \frac{π}{4} n = 0, \pm 1, \pm 2, \dots$
None of these

The correct answer is: $x equals n pi plus open parentheses negative 1 close parentheses to the power of n end exponent fraction numerator pi over denominator 4 end fraction minus fraction numerator pi over denominator 4 end fraction blank n equals 0 comma blank plus-or-minus 1 comma blank plus-or-minus 2 comma horizontal ellipsis$

$sin invisible function application x plus cos invisible function application x equals 1$
$rightwards double arrow fraction numerator 1 over denominator square root of 2 end fraction sin invisible function application x plus fraction numerator 1 over denominator square root of 2 end fraction cos invisible function application x equals fraction numerator 1 over denominator square root of 2 end fraction$
$rightwards double arrow sin invisible function application x cos invisible function application left parenthesis pi divided by 4 right parenthesis plus cos invisible function application x sin invisible function application left parenthesis pi divided by 4 right parenthesis equals sin invisible function application pi divided by 4$
$rightwards double arrow sin invisible function application left parenthesis x plus pi divided by 4 right parenthesis equals sin invisible function application pi divided by 4$
$rightwards double arrow x plus left parenthesis pi divided by 4 right parenthesis equals n pi plus open parentheses negative 1 close parentheses to the power of n end exponent blank pi divided by 4 comma blank n element of Z$
$rightwards double arrow x equals n pi plus left square bracket open parentheses negative 1 close parentheses to the power of n end exponent blank pi divided by 4 right square bracket minus pi divided by 4$
Where $n equals 0 comma blank plus-or-minus 1 comma blank plus-or-minus 2 comma horizontal ellipsis$

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