If =1- , then: - Vidyadip

MCQ

If $\tan\alpha=\frac{1-\cos\beta}{\sin\beta},$ then:

A
$\tan3\alpha=\tan2\beta$
✓
$\tan2\alpha=\tan\beta$
C
$\tan2\beta=\tan\alpha$
D
None of these

✓

Answer

Correct option: B.

$\tan2\alpha=\tan\beta$

$\tan\alpha=\frac{1-\cos\beta}{\sin\beta}$
$=\frac{2\sin^2\frac{\beta}{2}}{2\sin\frac{\beta}{2}\cos\frac{\beta}{2}}$
$=\frac{\sin\frac{\beta}{2}}{\cos\frac{\beta}{2}}$
$\Rightarrow\tan\alpha=\tan\frac{\beta}{2}$
$\Rightarrow\alpha=\frac{\beta}{2}$
$\Rightarrow2\alpha=\beta$
$\therefore\tan2\alpha=\tan\beta$

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

The value of $\mathop {\lim }\limits_{x \to \frac{\pi }{2}} \frac{{\int_{\pi /2}^x {t\,dt} }}{{\sin (2x - \pi )}}$ is

The term independent of $x$ in the expansion of ${(1 + x)^n}{\left( {1 + \frac{1}{x}} \right)^n}$ is

A circle passing through the point $P (\alpha, \beta)$ in the first quadrant touches the two coordinate axes at the points $A$ and $B$. The point $P$ is above the line $A B$. The point $Q$ on the line segment $A B$ is the foot of perpendicular from $P$ on $A B$. If $P Q$ is equal to $11$ units, then the value of $\alpha \beta$ is $.............$.

If for complex numbers ${z_1}$ and ${z_2}$, $arg({z_1}/{z_2}) = 0,$ then $|{z_1} - {z_2}|$ is equal to

The equation of the circumcircle of the triangle formed by the lines $y + \sqrt 3 x = 6,\;y - \sqrt 3 x = 6,$ and $y = 0$, is

If $\tan\text{x}=\text{x}+\frac{1}{4\text{x}},$ then $\sec\text{x}+\tan\text{x}=$

If the lines $ax + by + c = 0$, $bx + cy + a = 0$ and $cx + ay + b = 0$ be concurrent, then

How many numbers divisible by $5$ and lying between $3000$ and $4000$ can be formed from the digits $1,\, 2, \,3, \,4,\, 5,\, 6$ (repetition is not allowed)

$\mathop {Lim}\limits_{n\,\, \to \,\,\infty } $ $\frac{{{1^2}\,\,n\,\, + \,\,{2^2}\,\,(n\, - \,1)\,\, + \,\,{3^2}\,\,(n\, - \,2)\,\, + \,\,.....\,\, + \,\,{n^2}\,.\,\,1}}{{{1^3}\,\, + \,\,{2^3}\,\, + \,\,{3^3}\,\, + \,\,......\,\, + \,\,{n^3}}}$ is equal to :

If any tangent to the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$ cuts off intercepts of length $h$ and $k$ on the axes, then $\frac{{{a^2}}}{{{h^2}}} + \frac{{{b^2}}}{{{k^2}}} = $