SATHEE: Trigonometrical Equations 1 Question 17

Trigonometrical Equations 1 Question 17

17. The general solution of the trigonometric equation $\sin x + \cos x = 1$ is given by

(1981, 2M)

(a) $x = 2 n π; n = 0, \pm 1, \pm 2, \dots$

(b) $x = 2 n π + π / 2; n = 0, \pm 1, \pm 2, \dots$

(d) None of the above

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Answer:

Correct Answer: 17. (c)

Solution:

Given, $\sin x + \cos x = 1$

On dividing and multiplying each terms by $\sqrt{2}$ , we get

$\begin{array}{lc} \frac{1}{\sqrt{2}} \sin x + \frac{1}{\sqrt{2}} \cos x = \frac{1}{\sqrt{2}} \\ \Rightarrow & \sin x \cos \frac{π}{4} = \cos x \sin \frac{π}{4} = \frac{1}{\sqrt{2}} \\ \Rightarrow & \sin x + \frac{π}{4} = \sin \frac{π}{4} \\ \Rightarrow & x + \frac{π}{4} = n π + (- 1)^{n} \frac{π}{4} \\ \Rightarrow & x = n π + (- 1)^{n} \frac{π}{4} - \frac{π}{4}, n \in I \end{array}$

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Trigonometrical Equations 1 Question 17

17. The general solution of the trigonometric equation sin⁡x+cos⁡x=1 is given by

Answer:

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17. The general solution of the trigonometric equation $\sin x + \cos x = 1$ is given by