Prove that: ( ^3x+ ) +( 3x- ) =0 - Vidyadip

Question

Prove that:
$(\sin^3\text{x}+\sin\text{x})\sin\text{x}+(\cos3\text{x}-\cos\text{x})\cos\text{x}=0$

✓

Answer

$\text{LHS}=(\sin3\text{A}+\sin\text{A})\sin\text{A}(\cos3\text{A}-\cos\text{A})\cos\text{A}$
$\Rightarrow2\sin2\text{A}.\cos\text{A}.\sin\text{A}+(-2\sin2\text{A}.\sin\text{A}\cos\text{A})$ $\begin{bmatrix}\because\sin\text{C}+\sin\text{D}=2\sin\frac{\text{C+D}}{2}.\cos\frac{\text{C}-\text{D}}{2}\\\cos\text{C}-\cos\text{D}=-2\sin\frac{\text{C+D}}{2}.\sin\frac{\text{C+D}}{2}\end{bmatrix}$
$\Rightarrow2\sin2\text{A}.\cos\text{A}.\sin\text{A}-2\sin2\text{A}\cos\text{A}.\sin\text{A}$
$\Rightarrow0=\text{RHS}$

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 "2 Marks Questions" from Trigonometric Ratios Of Compound Angles→Trigonometric Ratios Of Compound Angles — all question types→MATHS STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

A card is drawn at random from a pack of 52 cards, find the probability that the card drawn is:

Not a black card

A card is drawn at random from a pack of 52 cards, find the probability that the card drawn is:

A diamond card

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{\text{e}^\text{ x }-\text{e }^{\sin\text{x}}}{\text{x}-\sin\text{x}}$

Calculate the value of $\lim _{x \rightarrow a} \frac{a \sin x-x \sin a}{a x^2-a^2 x}.$

Prove by direct method that for any real numbers x, y if x = y, then x² = y².

How many numbers of six digits can be formed from the digits 0, 1, 3, 5, 7 and 9 when no digit is repeated? How many of them are divisible by 10?

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow{\text{a}}}\frac{\text{logx}-\text{loga}}{\text{x}-\text{a}}$

Find the 20^th and n^thterms of the G.P. $\frac { 5 } { 2 } , \frac { 5 } { 4 } , \frac { 5 } { 8 }$ .......

In a $\triangle\text{ABC},$ if a = 5, b = 6 and C = 60^°, show that its area is $\frac{15\sqrt{3}}{2}\text{ sq. units.}$

Three coins are tossed once. Let A denote the event three heads show, B denote the event two heads and one tail show, C denote the event three tails show and D denote the event a head shows on the first coin. find Mutually exclusive?