Set of values of x satisfying equation, {2^{tan ,,left( {x,, - ,,{textstyle{π over 4}}} right

English

Gujarati

Hindi

Trigonometrical Equations

normal

The set of values of $x$ satisfying the equation,${2^{\tan \,\,\left( {x\,\, - \,\,{\textstyle{\pi \over 4}}} \right)}}$ $- 2$${\left( {0.25} \right)^{\frac{{{{\sin }^2}\,\left( {x\,\, - \,\,{\textstyle{\pi \over 4}}} \right)}}{{\cos \,\,2x}}}}$ $+ 1 = 0$, is :

A

an empty set

B

a singleton

C

a set containing two values

D

an infinite set

Solution

simplifies to ${2^{\tan \,\,\left( {x\,\, – \,\,{\textstyle{\pi \over 4}}} \right)}}$ $= 1$ $\Rightarrow x = \pi /4$ which is not possible

Standard 11

Mathematics

Share

Similar Questions

The number of solution of the equation $2\cos ({e^x}) = {5^x} + {5^{ – x}}$, are

easy

(IIT-1992)

If $S = \left\{ {x \in \left[ {0,2\pi } \right]:\left| {\begin{array}{*{20}{c}}
0&{\cos {\mkern 1mu} x}&{ – \sin {\mkern 1mu} x}\\
{\sin {\mkern 1mu} x}&0&{\cos {\mkern 1mu} x}\\
{\cos {\mkern 1mu} x}&{\sin {\mkern 1mu} x}&0
\end{array}} \right| = 0} \right\},$ then $\sum\limits_{x \in S} {\tan \left( {\frac{\pi }{3} + x} \right)} $ is equal to

hard

(JEE MAIN-2017)

The number of distinct solutions of the equation $\frac{5}{4} \cos ^2 2 x+\cos ^4 x+\sin ^4 x+\cos ^6 x+\sin ^6 x=2$ in the interval $[0,2 \pi]$ is

normal

(IIT-2015)

The number of values of $x$ in the interval $[0, 5 \pi ] $ satisfying the equation $3{\sin ^2}x – 7\sin x + 2 = 0$ is

medium

(IIT-1998)

Let $f:[0,2] \rightarrow R$ be the function defined by

$f ( x )=(3-\sin (2 \pi x )) \sin \left(\pi x -\frac{\pi}{4}\right)-\sin \left(3 \pi x +\frac{\pi}{4}\right)$

If $\alpha, \beta \in[0,2]$ are such that $\{x \in[0,2]: f(x) \geq 0\}=[\alpha, \beta]$, then the value of $\beta-\alpha$ is. . . . . . . . .

normal

(IIT-2020)