(m + 2) + (2m - 1) = 2m + 1, if - Vidyadip

MCQ

$(m + 2)\sin \theta + (2m - 1)\cos \theta = 2m + 1,$ if

A
$\tan \theta = \frac{3}{4}$
✓
$\tan \theta = \frac{4}{3}$
C
$\tan \theta = \frac{{2m}}{{{m^2} + 1}}$
D
None of these

✓

Answer

Correct option: B.

$\tan \theta = \frac{4}{3}$

b
(b) Squaring the given relation and putting $\tan \theta = t,$

${(m + 2)^2}\,{t^2} + 2(m + 2)\,(2m - 1)t + {(2m - 1)^2} = {(2m + 1)^2}\,(1 + {t^2})$

$ \Rightarrow \,3\,(1 - {m^2})\,{t^2} + (4{m^2} + 6m - 4)\,t - 8m = 0$

$ \Rightarrow \,(3t - 4)\,[(1 - {m^2})\,t + 2m] = 0$,

which is true, if $t = \tan \theta = \frac{4}{3}$ or $\tan \theta = \frac{{2m}}{{{m^2} - 1}}$.

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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The vertex of the parabola ${x^2} + 8x + 12y + 4 = 0$ is

If $A + B + C = {180^o},$ then $\sum {\tan \frac{A}{2}\tan \frac{B}{2} = } $

If the graph of $y = ax^3 + bx^2 + cx + d$ is symmetric about the line $x = k$ then

Let $\sum\limits_{k = 1}^{10} {f\,(a\, + \,k)} \, = \,16\,({2^{10}}\, - \,1),$ where the function $f$ satisfies $f(x + y) = f(x) f(y)$ for all natural numbers $x, y$ and $f(1) = 2.$ Then the natural number $‘ a '$ is

If $z = x + iy$ satisfies $|z|-2=0$ and $|z-i|-|z+5 i|=0$, then

If the lines $x\,=\,ay\,+\,b,\,\,z\,=\,cy\,+\,d$ and $x\, = \,a\,'z + \,b\,',\,\,y = \,c\,'z\, + \,d\,'$ are perpendicular, then

If ${\sin ^2}\theta - 2\cos \theta + \frac{1}{4} = 0,$ then the general value of $\theta $ is

The sum to $n$ terms of $(2n - 1) + 2\,(2n - 3)$ $ + 3\,(2n - 5) + .....$ is

If $P$ is a point on the hyperbola $16{x^2} - 9{y^2} = 144$ whose foci are ${S_1}$ and ${S_2}$, then $P{S_1}- P{S_2} = $

Let $\mathrm{g}: \mathrm{N} \rightarrow \mathrm{N}$ be defined as

$g(3 n+1)=3 n+2$

$g(3 n+2)=3 n+3$

$g(3 n+3)=3 n+1, \text { for all } n \geq 0$

Then which of the following statements is true?