The expression, , ( 3 , 2 , , - , , ) , , , , ( 3 , 2 , , - , , )… - Vidyadip

MCQ

The expression,$\frac{{\tan \,\left( {{\textstyle{{3\,\pi } \over 2}}\,\, - \,\,\alpha } \right)\,\,\,\cos \,\left( {{\textstyle{{3\,\pi } \over 2}}\,\, - \,\,\alpha } \right)}}{{\cos \,(2\,\pi \,\, - \,\alpha )}}$ $+ cos \left( {\alpha \,\, - \,\,\frac{\pi }{2}} \right) \,sin (\pi -\alpha ) + cos (\pi +\alpha ) sin \,\left( {\alpha \,\, - \,\,\frac{\pi }{2}} \right)$ when simplified reduces to :

✓
$0$
B
$1$
C
$-1$
D
none

✓

Answer

Correct option: A.

$0$

a
$\frac{{ - \,\cot \alpha \,\,\sin \alpha }}{{\cos \alpha }} + sin\alpha . sin\alpha + cos\alpha . cos\alpha = -1+1 = 0$

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

If $X$ and $Y$ are two independent binomial variates, satisfying $B\left( {10,\frac{1}{2}} \right)$ and $B\left( {8,\frac{1}{2}} \right)$ respectively, then probability $P\left( {X + Y = 2} \right)$ is

Let $f(x) = e^x -x$ and $g(x) = x^2 -x$, $\forall \in R$. Then the set of all $x \in R$, where the function $h(x) = (fog)\, (x)$ is increasing is

Let $y(x)$ be the solution of the differential equation $2 x^{2} d y+\left(e^{y}-2 x\right) d x=0, x>0$. If $y(e)=1$, then $\mathrm{y}(1)$ is equal to :

$\frac{{{{( - 1 + i\sqrt 3 )}^{15}}}}{{{{(1 - i)}^{20}}}} + \frac{{{{( - 1 - i\sqrt 3 )}^{15}}}}{{{{(1 + i)}^{20}}}}$ is equal to

The value of $\int\limits_{ - 7}^7 {\frac{{{5^x}}}{{{5^{[x]}}}}dx} $ is equal to (where $[.]$ denotes greatest integer function)

For any $3 \times 3$ matrix $M$, let $|M|$ denote the determinant of $M$. Let $I$ be the $3 \times 3$ identity matrix. Let $E$ and $F$ be two $3 \times 3$ matrices such that $(I-E F)$ is invertible. If $G=(I-E F)^{-1}$, then which of the following statements is (are) $TRUE$ ?

$(A)$ $| FE |=| I - FE || FGE |$

$(B)$ $| I - FE |( I + FGE )= I$

$(C)$ $EFG = GEF$

$(D)$ $( I - FE )( I - FGE )= I$

If $a $ and $b $ are two unit vectors such that $a+2b$ and $5a - 4b$ are perpendicular to each other, then the angle between $a$ and $b $ is ............. $^o$

$\int_{0}^{\frac{1}{3}} (\sum_{r=0}^{101}\{x + \frac{r}{3}\})dx$ is equal to (where {.} represents fractional part function)

In the binomial expansion of ${\left( {a - b} \right)^n},n \ge 5,\;$ the sum of $5^{th}$ and $6^{th}$ terms is zero , then $a/b$ equals.

If the equation $\cos ^{4} \theta+\sin ^{4} \theta+\lambda=0$ has real solutions for $\theta,$ then $\lambda$ lies in the interval