Choose the correct answer. The value of 75^ - 75^ is equal to: - Vidyadip

MCQ

Choose the correct answer. The value of $\tan75^\circ-\cot75^\circ$ is equal to:

✓
$2\sqrt{3}$
B
$2+\sqrt{3}$
C
$2-\sqrt{3}$
D
$1$

✓

Answer

Correct option: A.

$2\sqrt{3}$

$\tan75^\circ-\cot75^\circ=\frac{\sin75^\circ}{\cos75^\circ}-\frac{\cos75^\circ}{\sin75^\circ}\\=\frac{2(\sin^275^\circ-\cos^275^\circ)}{2\sin75^\circ\cos75^\circ}$
$=\frac{-2\cos150^\circ}{\sin150^\circ}$
$=-2\cot150^\circ$
$=-2\cot(180^\circ-30^\circ)$
$=2\cot30^\circ$
$=2\sqrt3$

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 "M.C.Q (1 Marks)" 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

Number of all four digit numbers having different digits formed of the digits $1, 2, 3, 4$ and $5$ and divisible by $4$ is:

The equation of the base of an equilateral triangle is $x + y = 2$ and the vertex is $(2, -1)$. The length of the side of the triangle is

The mean of five observations is $5$ and their variance is $9.20$. If three of the given five observations are $1, 3$ and $8$, then a ratio of other two observations is

The straight line joining any point $P $ on the parabola $y^2 = 4ax $ to the vertex and perpendicular from the focus to the tangent at $P$, intersect at $R$, then the equaiton of the locus of $R$ is

Let $\mathrm{P}$ be a parabola with vertex $(2,3)$ and directrix $2 x+y=6$. Let an ellipse $E: \frac{x^2}{a^2}+\frac{y^2}{b^2}=1, a>b$ of eccentricity $\frac{1}{\sqrt{2}}$ pass through the focus of the parabola $\mathrm{P}$. Then the square of the length of the latus rectum of $\mathrm{E}$, is

If $n$ is a positive integer, then ${(1 + i)^n} + {(1 - i)^n}$ is equal to

Let $A(a, b), B(3,4)$ and $(-6,-8)$ respectively denote the centroid, circumcentre and orthocentre of a triangle. Then, the distance of the point $P(2 a+3,7 b+5)$ from the line $2 x+3 y-4=0$ measured parallel to the line $x-2 y-1=0$ is

Sum of $n$ terms of the series $\sqrt{2}+\sqrt{8}+\sqrt{18}+\sqrt{32}+\ ...\text{ is}$

The lines $15x - 18y + 1 = 0,$ $12x + 10y - 3 = 0$ and $6x + 66y - 11 = 0$ are

Which one of the following equations represented parametrically, represents equation to a parabolic profile ?