Solve the following equations: + =2 - Vidyadip

Question

Solve the following equations:
$\sin\text{x}+\cos\text{x}=\sqrt{2}$

✓

Answer

We have,
$\sin\text{x}+\cos\text{x}=\sqrt{2}$
$\Rightarrow\frac{1}{\sqrt{2}}\sin\text{x}+\frac{1}{\sqrt{2}}\cos\text{x}=1$
$\Rightarrow\sin\frac{\pi}{4}\sin\text{x}+\cos\frac{\pi}{4}\cos\text{x}=1$$\Big[\because\cos\frac{\pi}{4}=\sin\frac{\pi}{4}=\frac{1}{\sqrt{3}}\Big]$
$\Rightarrow\cos\Big(\text{x}-\frac{\pi}{4}\Big)=\cos0^\circ$
$\Rightarrow\text{x}-\frac{\pi}{4}=2\text{n}\pi,\text{n}\in\text{z}$
$\Rightarrow\text{x}=2\text{n}\pi+\frac{\pi}{4},\text{n}\in\text{z}$
$\therefore\text{x}=(8\text{n}+1)\frac{\pi}{4},\text{n}\in\text{z}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "5 Marks Questions" from Trigonometric Equations→Trigonometric Equations — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

Given $\text{a}_1=\frac{1}{2}\Big(\text{a}_0+\frac{\text{A}}{\text{a}_0}\Big),\text{a}_2=\frac{1}{2}\Big(\text{a}_1+\frac{\text{A}}{\text{a}_1}\Big)$ and $\text{a}_{\text{n}+1}=\frac{1}{2}\Big(\text{a}_\text{n}+\frac{\text{A}}{\text{a}_\text{n}}\Big)$ for $\text{n}\geq2,$ Where a > 0, A > 0. Prove that $\frac{\text{a}_{\text{n}}-\sqrt{\text{A}}}{{\text{a}_{\text{n}}+\sqrt{\text{A}}}}=\Bigg(\frac{\text{a}_{\text{1}}-\sqrt{\text{A}}}{\text{a}_{\text{1}}+\sqrt{\text{A}}}\Bigg)^{2^{\text{n}-1}}$

Find the equation to the ellipse in the following case:
eccentricity $\text{e}=\frac{1}{2}$ and lenght of latus-rectum = 5

Differentiate If $y=\sqrt{\frac{\sec x-\tan x}{\sec x+\tan x}}$ show that $\frac{d y}{d x}=\sec x(\tan x+\sec x)$

Prove that: $\frac{\sin\text{(A-B)}}{\sin\text{A}\sin\text{B}}+\frac{\sin\text{(B-C)}}{\sin\text{B}\sin\text{C}}+\frac{\sin\text{(C-A)}}{\sin\text{C}\sin\text{A}}=0$

If $z_1$ is a complex number other than -1 such that $|\text{z}|=1$ and $\text{z}_2=\frac{\text{z}_1-1}{\text{z}_1+1},$ then show that the real parts of $z_2$ is zero.

Let f and g be two real functions defined by $\text{f(x)}=\sqrt{\text{x}+1}$ and $\text{g(x)}=\sqrt{9-\text{x}^2}$ Then describe the following functions:
$\text{f}^2+7\text{f}$

If P(11, r) = P(12, r − 1) find r.

Evaluate the following limit:
$\lim\limits_{\text{n}\rightarrow\infty}{\Big(\frac{1}{\text{n}^2}+\frac{2}{\text{n}^2}+\frac{3}{\text{n}^2}+\ \cdots+\frac{\text{n}-1}{\text{n}^2}}{}\Big)$

Calculate the mean deviation about the median of the following observation:
$38, 70, 48, 34, 42, 55, 63, 46, 54, 44$

If $f(x) = x^2 - 3x + 4$, then find the values of x satisfying the equation $f(x) = f(2x + 1).$