The general value of satisfying ^2 + = 2 is - Vidyadip

MCQ

The general value of $\theta $ satisfying ${\sin ^2}\theta + \sin \theta = 2$ is

A
$n\pi + {( - 1)^n}\frac{\pi }{6}$
B
$2n\pi + \frac{\pi }{4}$
✓
$n\pi + {( - 1)^n}\frac{\pi }{2}$
D
$n\pi + {( - 1)^n}\frac{\pi }{3}$

✓

Answer

Correct option: C.

$n\pi + {( - 1)^n}\frac{\pi }{2}$

c
(c) ${\sin ^2}\theta + \sin \theta - 2 = 0$

$\Rightarrow (\sin \theta - 1)\,(\sin \theta + 2) = 0$

$ \Rightarrow $ $\sin \theta \ne - 2$ ,

$\therefore \,\,\sin \theta = 1 = \sin \pi /2$

$ \Rightarrow $ $\theta = n\pi + {( - 1)^n}\frac{\pi }{2}$.

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

Let $A B$ be a line segment of length $2$ . Construct a semicircle $S$ with $A B$ as diameter. Let $C$ be the mid-point of the $\operatorname{arc} A B$. Construct another semicircle $T$ external to the $\triangle A B C$ with chord $A C$ as diameter. The area of the region inside the semi-circle $T$ but outside $S$ is

If $I_{m, n}=\int_{0}^{1} x^{m-1}(1-x)^{n-1} d x,$ for $m, n \geq 1$ and $\int_{0}^{1} \frac{x^{m-1}+x^{n-1}}{(1+x)^{m+n}} d x=\alpha I_{m, n}, \alpha \in R,$ then $\alpha$ equals .... .

Let $\vec a = 3\hat i + 2\hat j + 2\hat k$ and $\vec b = \hat i + 2\hat j - 2\hat k$ be two vectors. If a vector perpendicular to both the vectors $\vec a + \vec b$ and $\vec a - \vec b$ has the magnitude $12$ then one such vector is

The graphs of $f (x) = x^2 \,\& \,g(x) = cx^3 \,\, (c > 0)$ intersect at the points $(0, 0) \& \left( {\frac{1}{c},\,\,\frac{1}{{{c^2}}}} \right)$. If the region which lies between these graphs & over the interval $[0, 1/c]$ has the area equal to $2/3$ then the value of $c$ is

The value of $\int_0^2 {\frac{{{3^{\sqrt x }}}}{{\sqrt x }}} \,dx$ is

Let ${a_2},{a_3} \in R$ such that $\left| {{a_2} - {a_3}} \right| = 6$ and $f\left( x \right) = \left| {\begin{array}{*{20}{c}}
1&{{a_3}}&{{a_2}}\\
1&{{a_3}}&{2{a_2} - x}\\
1&{2{a_3} - x}&{{a_2}}
\end{array}} \right|,x \in R.$ Then the greatest value of $f(x)$ is

The points $(1,{\rm{ }}1)$, $(0,{\sec ^2}\theta ),\,({\rm{cose}}{{\rm{c}}^2}\theta ,{\rm{ }}0)$ are collinear for

Let $f(x)=\int_0^x t\left(t^2-9 t+20\right) d t, \quad 1 \leq x \leq 5$. If the range of $f$ is $[\alpha, \beta]$, then $4(\alpha+\beta)$ equals:

In a $G.P.$ the sum of three numbers is $14$, if $1 $ is added to first two numbers and subtracted from third number, the series becomes $A.P.$, then the greatest number is

$A =\{ x_1, x_2, x_3, x_4 \}; \,\,$$B = \{ y, y_2, y_3, y_4 \} .$ A function is defined from set $A$ to set $B.$ Number of one-one function such that $f(x_i) \ne y_i$ for $i = 1, 2, 3, 4$ is equal to :