The general solution of sin x-cos x-2- for any integer n is A- 2 n-1 -B- n -C- 2 n -D- 2 n -3 -4

The correct option is D Given that, sin x – cos x = √(2) ⇒1/√(2)sin x 1/√(2)cos x = 1 ⇒cos ( x + π/4 ) = 1 ⇒cos ( x + π/4 ) = cos(π) ⇒ x + π/4 = 2nπ±π ...

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Standard XI

Mathematics

Equations of the form acos?+bsin? = c

The general s...

Question

The general solution of $sin x - cos x = \sqrt{2},$ for any integer n is

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Solution

The correct option is B
Given that, $sin x - cos x = \sqrt{2}$
$\Rightarrow \frac{1}{\sqrt{2}} sin x - \frac{1}{\sqrt{2}} cos x = 1$
$\Rightarrow cos (x + \frac{π}{4}) = - 1$
$\Rightarrow cos (x + \frac{π}{4}) = cos (π)$
$\Rightarrow x + \frac{π}{4} = 2 n π \pm π$
$\Rightarrow x = 2 n π + \frac{3 π}{4}, 2 n π - \frac{5 π}{4}$

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The general solution of sinx−cosx=√2, for any integer n is

The correct option is B Given that, sinx–cosx=√2 ⇒1√2sinx−1√2cosx=1 ​⇒cos(x+π4)=−1 ​⇒cos(x+π4)=cos(π) ​⇒x+π4=2nπ±π ​⇒x=2nπ+3π4,2nπ−5π4

The general solution of $sin x - cos x = \sqrt{2},$ for any integer n is