Solve the following equations: -3 2x+ 3x= -3 2x+ 3x - Vidyadip

Question

Solve the following equations:
$\sin\text{x}-3\sin2\text{x}+\sin3\text{x}=\cos\text{x}-3\cos2\text{x}+\cos3\text{x}$

✓

Answer

$\sin\text{x}-3\sin2\text{x}+\sin3\text{x}=\cos\text{x}-3\cos2\text{x}+\cos3\text{x}$
$(\sin\text{x}+\sin3\text{x})-3\sin2\text{x}-(\cos\text{x}+\cos3\text{x})+3\cos2\text{x}=0$
$2\sin2\text{x}\cos\text{x}-3\sin2\text{x}-2\cos2\text{x}\cos\text{x}+3\cos2\text{x}=0$
$\sin2\text{x}(2\cos\text{x}-3)-\cos2\text{x}(2\cos\text{x}-3)=0$
$(2\cos\text{x}-3)(\sin2\text{x}-\cos2\text{x})=0$
$\cos\text{x}=\frac{3}{2}$ or $\sin2\text{x}-\cos2\text{x}-\cos2\text{x}=0$
but $\cos\text{x}\in[-11]\Rightarrow\cos\text{x}\not=\frac{3}{2}$
$\sin2\text{x}=\cos2\text{x}$
$2\text{x}=\text{n}\pi+\frac{\pi}{4}$
$\text{x}=\frac{\text{n}\pi}{2}+\frac{\pi}{8}$

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 Functions→Trigonometric Functions — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

Table below shows the frequency $f$ with which $'x'$ alpha particles radiated from a diskette:

x	0	1	2	3	4	5	6	7	8	9	10	11	12
f	51	203	383	525	532	408	273	139	43	27	10	4	2

Calculate the mean and variance.

Prove the following:
$\sin2\text{x}+2\sin4\text{x}+\sin6\text{x}=4\cos^2\text{x}\sin4\text{x}$

Find the multiplicative inverse of the following complex numbers:
$\sqrt{5}-3\text{i}$

Solve the following systems of inequations graphically:
$2\text{x} + \text{y} \geq 8, \text{x} + 2\text{y} \geq 8,\text{ x} +\text{ y}\leq 6$

Find the sum of the following series to $n$ terms:
$3 \times 1^2 + 5 \times 2^2 + 7 \times 3^2 + ...$

How many different selections of $4$ books can be made from $10$ different books, if

There is no restriction.
Two particular books are always selected.
Two particular books are never selected?

Find the equations of the lines through the point of intersection of the lines $x - y + 1 = 0$ and $2x - 3y + 5 = 0$ and whose distance from the point $(3, 2)$ is $\frac{7}{5}$.

Prove that $\stackrel{{7+77+777+...+777\ ...................\ 7}}{ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \hbox{ n-digits}}$ $$${ =\frac{7}{81}(10^{\text{n}+1}-9\text{n}-10)}$ for all $\text{n}\in\text{N}.$

Prove that:
$\sin\alpha+\sin\beta+\sin\gamma-\sin(\alpha+\beta+\gamma)\\=4\sin\Big(\frac{\alpha+\beta}{2}\Big)\sin\Big(\frac{\beta+\gamma}{2}\Big)\sin\Big(\frac{\gamma+\alpha}{2}\Big)$

If $2\tan\frac{\alpha}{2}=\tan\frac{\beta}{2},$ prove that $\cos\alpha=\frac{3+5\cos\beta}{5+3\cos\beta}$