Question

The number of solution of equation $si{n}^{100}x-co{s}^{100}x=1$ if $x\epsilon [0,2\pi ],$ is

• A. 1
• B. 4
• C. 2
• D. 0

Answer 1

The correct option is A 1

Given

${\sin }^{100}x-{\cos }^{100}x=1$

The range of ${\sin }^{100}x$ and ${\cos }^{100}x$ is $[0,1]$

To get sum The diifferecne as $1$

The Possibility is $(1,0)$

$⟹x=\frac{\pi }{2}$

$\therefore$ there is only one soluton.