recategorized by
274 views

1 Answer

0 votes
0 votes
$\underline{\textbf{Answer: B}\Rightarrow}$

$\underline{\textbf{Solution:}\Rightarrow}$

The above equation can be converted in the form of identity of the form:

$(a+b)^3 = a^3 + b^3 + 3ab(a+b)$

Let $a = \sin^2\frac{\pi}{81}, b = \cos^2\frac{\pi}{81}$

Now,

$=(\sin^2\frac{\pi}{81}+\cos^2\frac{\pi}{81})^3 = (\sin^2\frac{\pi}{81})^3 + (\sin^2\frac{\pi}{81})^3 + 3\sin^2\frac{\pi}{81}cos^2\frac{\pi}{81}\underbrace{(\sin^2\frac{\pi}{81}+\cos^2\frac{\pi}{81})}_\text{=1} = 1$

But the question has extra $-1$. So, answer = $1-1$ = 0

$\therefore \mathbf B$ is the correct option.
edited by

Related questions

0 votes
0 votes
2 answers
1
gatecse asked Sep 18, 2019
797 views
If $\tan x=p+1$ and $\tan y=p-1$, then the value of $2 \cot (x-y)$ is$2p$$p^2$$(p+1)(p-1)$$\frac{2p}{p^2-1}$
0 votes
0 votes
0 answers
2
gatecse asked Sep 18, 2019
673 views
The equations $x=a \cos \theta + b \sin \theta$ and $y=a \sin \theta + b \cos \theta$, $( 0 \leq \theta \leq 2 \pi$ and $a,b$ are arbitrary constants) representa circlea ...
0 votes
0 votes
1 answer
3
gatecse asked Sep 18, 2019
462 views
If in a $\Delta ABC$, $\angle B = \frac{2 \pi}{3}$, then $\cos A + \cos C$ lies in$[\:- \sqrt{3}, \sqrt{3}\:]$$(\: – \sqrt{3}, \sqrt{3}\:]$$(\:\frac{3}{2}, \sqrt{3}\:)$...
0 votes
0 votes
0 answers
4
gatecse asked Sep 18, 2019
204 views
The number of values of $x$ for which the equation $\cos x = \sqrt{\sin x} – \dfrac{1}{\sqrt{\sin x}}$ is satisfied, is$1$$2$$3$more than $3$