_ r = 1 ^ 89 _3 ( , , r^o ) = - Vidyadip

Question

$\sum\limits_{r = 1}^{89} {{{\log }_3}(\tan \,\,{r^o})} = $

✓

Answer

d
(d) $\sum\limits_{r = 1}^{39} {{{\log }_3}(\tan {r^o}) = {{\log }_3}(\tan {{45}^o}} ) = {\log _3}1 = 0$.

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

The value of $p$ for which the sum of the squares of the roots of equation $x^2 -(p + 3)x + (5p\ -2) = 0$ assume its least value is

If $a_1, a_2, a_3 …………$ an are in $A.P$ and $a_1 + a_4 + a_7 + …………… + a_{16} = 114$, then $a_1 + a_6 + a_{11} + a_{16}$ is equal to

Three balls are drawn at random from a bag containing 5 blue and 4 yellow balls. Let the random variables X and Y respectively denote the number of blue and Yellow balls. If $\bar{X}$ and $\bar{Y}$ are the means of $X$ and $Y$ respectively, then $7 \bar{X}+4 \bar{Y}$ is equal to _____________ .

If $n(U)$ = $600$ , $n(A)$ = $100$ , $n(B)$ = $200$ and $n(A \cap B )$ = $50$, then $n(\bar A \cap \bar B )$ is

($U$ is universal set and $A$ and $B$ are subsets of $U$)

The constant term in the expansion of $\left(2 x+\frac{1}{x^7}+3 x^2\right)^5 \text { is }........$.

Number of solutions of $5$ $cos^2 \theta -3 sin^2 \theta + 6 sin \theta cos \theta = 7$ in the interval $[0, 2 \pi] $ is :-

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

The mean of the data set comprising of $16$ observations is $16.$ If one of the observation valued $16$ is deleted and three new observations valued $3, 4$ and $5$ are added to the data, then the mean of the resultant data, is:

A line which makes angle ${60^o}$ with $y$ - axis and $z$ - axis, then the angle which it makes with $x$ -axis is ......... $^o$

For three positive integers $p , q , r , x ^{ pq p ^2}= y ^{ qr }= z ^{ p ^2 r }$ and $r=p q+1$ such that $3,3 \log _y x, 3 \log _z y, 7 \log _x z$ are in A.P. with common difference $\frac{1}{2}$. Then $r - p - q$ is equal to