Prove the following. (3+1)(3- 30^ )= ^360^ -2 60^ - Vidyadip

Question

Prove the following.
$(\sqrt{3}+1)(3-\cot30^\circ)=\tan^360^\circ-2\sin60^\circ$

✓

Answer

RHS $=\tan^360^\circ-2\sin60^\circ=(\sqrt{3})^3-2\frac{\sqrt{3}}{2}=3\sqrt{3}-\sqrt{3}=2\sqrt{3}$
LHS $=(\sqrt{3}+1)(3-\cot30^\circ)=(\sqrt{3}+1)(3-\sqrt{3})$
$[\because\ \tan60^\circ=\sqrt{3}\sin60^\circ=\frac{\sqrt{3}}{2}\text{ and }=(\sqrt{3}+1)\sqrt{3}(\sqrt{3}-1)\cot30^\circ=\sqrt{3}]$
$=(\sqrt{3}(\sqrt{3})^2-1)=\sqrt{3}(3-1)=2\sqrt{3}$
$\therefore$ 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 "3 Marks Question" from Introduction of Trigonometry and its Application→Introduction of Trigonometry and its Application — all question types→Maths STD 10 question papers→CBSE Board STD 10 question papers→CBSE Board question paper generator→

Similar questions

Prove that: $(\operatorname{cosec} A-\sin A)(\sec A-\cos A) =\frac{1}{\tan A+\cos A}$

If $\tan\theta=\frac{\text{a}}{\text{b}},$ prove that $\frac{\text{a}\sin\theta+\text{b}\cos\theta}{\text{a}\sin\theta+\text{b}\cos\theta}=\frac{\text{a}^2-\text{b}^2}{\text{a}^2+\text{b}^2}.$

If the sides of a triangle are $3\ cm, 4\ cm$ and $6\ cm$ long, determine whether the triangle is a right-angled triangle.

Three vertices of a parallelogram are (a + b, a - b), (2a + b, 2a - b), (a - b, a + b). Find the fourth vertex.

Out of the two concentric circles, the radius of the outer circle is $5 \ cm$ and the chord $AC$ of length $8 \ cm$ is a tangent to the inner circle. Find the radius of the inner circle.

Find the sum of the following arithmetic progressions:
$a + b, a - b, a - ab, ....$. to $22$ terms.

If $\text{x}=\text{a}\sin\theta\text{ and y}=\text{b}\cos\theta,$ what is the value pf $b^2x^2 + a^2y^2?$

One zero of the polynomial $x^2-2 x-(7 p+3)$ is $-1 ,$ find the value of $p$ and the other zero.

Find the value of $p$ for which the points $(-5,1)$, $(1, p)$ and $( 4,-2 )$ are collinear.

In annual examination, marks (out of 90) obtained by students of class IX in mathematics are given below:

Marks	0-15	15-30	30-45	45-60	60-75	75-90
Number of students	2	4	5	20	9	10

Find the mean marks of the student.