[problem]
I got following equation of a circle..
$x^2+y^2=9 ..(1)$
and a equation of curve as follows..
$\tan^4x + \cot^4 x + 2 =4\sin^2y....(2)$
I have to find points which satisfy both the equation..i.e points which are on the curve and inscribed inside or on the circle in common
[ My approach]
For solving following equation I first equate for trignometric function,So that i can obtain equation(2) in terms of x and y...Mathmetically I targeted for this.
$y=\frac {\arcsin \sqrt(\tan^4x + \cot^4 x + 2 )} 2$ (from equation (2))
I am trying to equate $\sqrt(\tan^4x + \cot^4 x + 2 )$ in terms of $\sin a$ where "a" is any polynomial expression ..
[HELP]
How should i do so..I cant break that in terms or sin function..It's going lengthy and complex . Or if any other less costly approach could be made
Hint:
For real $x,$
$$\dfrac{\tan^4x+\cot^4x}2\ge\sqrt{\tan^4x\cot^4x}=?$$
$$\implies\sin^2y\ge1\implies\sin^2y=1$$ for real$y$