If A = 30^ , verify that 2 A=2 A 1+ ^2 A - Vidyadip

Question

If $A = 30^\circ,$ verify that $\sin 2 A=\frac{2 \tan A}{1+\tan ^2 A}$

✓

Answer

$LHS =\sin 2A$
Putting $A = 30^\circ$ in $LHS$ and $RHS.,$ we get
LHS = sin 2 x 30° = sin 60° $=\frac{\sqrt{3}}{2}$
$\text { RHS }=\frac{2 \times \tan 30^{\circ}}{1+\tan ^2 30^{\circ}}=\frac{2 \times \frac{1}{\sqrt{3}}}{1+\left(\frac{1}{\sqrt{3}}\right)^2}$
$=\frac{\frac{2}{\sqrt{3}}}{1+\frac{1}{3}} \cdot \frac{2}{\frac{4}{3}}$
$=\frac{2 \times 3}{\sqrt{3} \times 4}=\frac{\sqrt{3}}{4}$
Hence,
$LHS = RHS$
Hence proved.

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 Mark Question Answer]" from Trigonometry→Trigonometry — all question types→Mathematics STD 10 question papers→ICSE Board STD 10 question papers→ICSE Board question paper generator→

Similar questions

Evaluate : $3 \frac{\sin 72^{\circ}}{\cos 18^{\circ}}-\frac{\sec 32^{\circ}}{\operatorname{cosec} 58^{\circ}}$

The locus of points within a circle that are equidistant from the end points of a given chord.

Find the value of $‘K’$ for which $x = 3$ is a solution of the quadratic equation, $(K + 2)x^2 – Kx + 6 = 0$. Also, find the other root of the equation.

A card is drawn from a pack of 52 cards. Find the probability that the card drawn is : an ace

Solve for x in the following in-equation, if the replacement set is R;
$2x - 3 < 7$

If $a : b :: c : d$, prove that $\frac{2 a+5 b}{2 a-5 b}=\frac{2 c+5 d}{2 c-5 d}$

Describe completely the locus of point in the following cases:
Centre of a ball, rolling along a straight line on a level floor.

Hundred identical cards are numbered from 1 to 100. The cards The cards are well shuffled and then a card is drawn. Find the probability that the number on card drawn is : between 40 and 60

If $M =\left|\begin{array}{ll}8 & 3 \\ 9 & 7 \\ 4 & 3\end{array}\right|$ and $N =\left|\begin{array}{cc}4 & 7 \\ 5 & 3 \\ 10 & 1\end{array}\right|$ find $M - N$

Without using trigonometric table, evaluate:
$
\frac{\sin 72^{\circ}}{\cos 18^{\circ}}-\frac{\sec 32^{\circ}}{\operatorname{cosec} 58^{\circ}}
$