Solve the following equations: (3-1) +(3+1) =2 - Vidyadip

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 "(Each question 3 marks)" from Trigonometric Equations→Trigonometric Equations — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow0}\frac{\sin^24\text{x}^2}{\text{x}^4}$

If $P(n)$ is the statement " $2^n \geq 3 n$ " and if $P(r)$ is true, prove that $P(r+1)$ is true.

If (n + 2)! = 60 [(n - 1)!], find n.

Expand the given expression ${\left( {\frac{2}{x} - \frac{x}{2}} \right)^5}$

If $\frac{1}{\text{a}},\ \frac{1}{\text{b}},\ \frac{1}{\text{c}}$ are in A.P., Prove that: $\frac{\text{b}+\text{c}}{\text{a}},\ \frac{\text{c}+\text{a}}{\text{b}},\ \frac{\text{a}+\text{b}}{\text{c}}$ are in A.P.

If $\cos\text{A}=-\frac{24}{25},$ $\cos\text{B}=-\frac{12}{13},$ where A and B both lie in second quadrant,find the value of $\sin\text{(A+B)}$.

$\sin\text{(A+B)}$
$\cos\text{(A+B)}$

In a survey of 100 persons it was found that 28 read magazine A, 30 read magazine B, 42 read magazine C, 8 read magazines A and B, 10 read magazines A and C, 5 read magazines B and C and 3 read all the three magazines?

How many read none of three magazines?
How many read magazine C only?

Between 1 and $31, \mathrm{~m}$ numbers have been inserted in such a way that resulting sequence is an A.P. and the ratio of $7^{\text {th }}$ and $(m-1)^{\text {th }}$ numbers is $5: 9$. Find the value of $m$.

If A and B are two set having 3 elements in common. If n(A) = 5, n(B) = 4, find n(A × B) and $\text{n}\big[(\text{A}\times\text{B})\cap(\text{B}\times\text{A})\big]$

Prove the following identities: $1-\frac{\sin^2\text{x}}{1+\cot\text{x}}-\frac{\cos^2\text{x}}{1+\tan\text{x}}=\sin\text{x}\cos\text{x}$