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 Equations→Trigonometric Equations — all question types→MATHS STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

Solve the following equations:
$2\sin^{2}\text{x}=3\cos\text{x},0\leq\text{x}\leq2\pi$

Find the equations to the straight lines passing through the point (2, 3) and inclined at and angle of 45° to the line 3x + y - 5 = 0.

Differentiate the following from first principle

$\tan(\text{2x}+1)$

If ${^8}\text{C}_{\text{r}}-{^7}\text{C}_{\text{3}}={^7}\text{C}_{\text{2}},$ Find r.

The variance of 15 bservation is 4. If each observation is increased by 9, find the variance of the resulting observation.

Prove that the family of lines represented by $\text{x}(1+\lambda)=\text{y}(2-\lambda)+5=0,$ $\lambda$ being arbitrary, pass through a fixed point. Also, find that point.

Prove that: $\tan 20^{\circ} \tan 30^{\circ} \tan 40^{\circ} \tan 80^{\circ}=1$

Prove the following by the principle of mathematical induction:

$\text{a}+(\text{a}+\text{d})+(\text{a}+2\text{d})...+(\text{a}+(\text{n}-1)\text{d})=\frac{\text{n}}{2}[2\text{a}+(\text{n}-1)\text{d}]$

Prove the following identities:
$\frac{\tan^3\text{x}}{1+\tan^2\text{x}}+\frac{\cot^3\text{x}}{1+\cot^2\text{x}}=\frac{1-2\sin^2\text{x}\cos^2\text{x}}{\sin\text{x}\cos\text{x}}$

If $\cos\theta+\tan\theta=2\text{cosec}\theta,$ then find the general value of $\theta.$