Download App

Trigonometric Equations — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsTrigonometric Equations3 Marks
Question
Solve the following equations:
$(\sqrt{3}-1)\cos\text{x}+(\sqrt{3}+1)\sin\text{x}=2$
✓

Answer

We have,
$(\sqrt{3}-1)\cos\text{x}+(\sqrt{3}+1)\sin\text{x}=2$
Divide on both side by $2\sqrt{2}$
$\frac{(\sqrt{3}-1)}{2\sqrt{2}}\cos\text{x}+\frac{(\sqrt{3}+1)}{2\sqrt{2}}\sin\text{x}=\frac{1}{\sqrt{2}}$
$\sin\Big(\text{x}+\tan^{-1}\Big(\frac{\sqrt{3}-1}{\sqrt{3}+1}\Big)\Big)=\sin\frac{\pi}{4}$
$\text{x}=2\text{n}\pi+\frac{\pi}{3}$ or $2\text{n}\pi-\frac{\pi}{6}\text{n}\in\text{z}$

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 "3 Marks Question" 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

There are 10 points in a plane of which 4 are collinear. How many different straight lines can be drawn by joining these points.
→
The sum of two numbers is 6 times their geometric means, show that the numbers are in the ratio $(3+2\sqrt{2}):\big(3-2\sqrt{2}\big).$
→
Find the rational number having the following decimal expansions:$0.\overline{3}$
→
Let $A = \{1, 2, 3, 4, 6\}.$ Let $R$ be the relation on $A$ defined by $\{(a, b): a, b \in A, b$ is exactly divisible by $a\}.$
  1. Write $R$ in roster form
  2. Find the domain of $R$
  3. Find the range of $R.$
→
Find the number of ways of selecting 9 balls from 6 red balls, 5 white balls and 5 blue balls if each selection consists of 3 balls of each colour.
→
If A = {1, 2, 3} and B = {2, 4}, what are A × B, B × A, A × A, B × B and $(\text{A}\times\text{B})\cap(\text{B}\times\text{A})?$
→
Solve the following linear inequations in R:
$\frac{\text{x}}{\text{x}-5}>\frac{1}{2}$
→
Evaluate:
$\lim\limits_{\text{x} \rightarrow \frac{\pi}{3}}\frac{\sqrt{1-\cos6}}{\sqrt{2}\bigg(\frac{\pi}{3}-\text{x}\bigg)} $
→
Find the square root of $3 - 4i$
→
Coefficient of variation of two distributions are 60% and 70% and their standard deviations are 21 and 16 respectively. What are their arithmetic means?
→