The number of solutions of the equation 1 + sin4 x = cos23x, [x [ - 5 2,5 2 ]] is :

Question

The number of solutions of the equation

1 + sin4
 x = cos23x, $$x \in \left[ { - {{5\pi } \over 2},{{5\pi } \over 2}} \right]$$ is :

Accepted Answer

$$\mathop {\underline {1 + {{\sin }^4}x} }\limits_{ \ge 1}  = \mathop {\underline {{{\cos }^2}3x} }\limits_{ \le 1} $$

Now for equality to hold sin4x = 0 \& cos23x = 1

sin4 = 0 $$ \Rightarrow $$ x = -2$$\pi $$, - $$\pi $$, 0, $$\pi $$, 2$$\pi $$

All of which satisfy cos23x = 1 $$ \Rightarrow $$ 5 solutions

Solutions · 1