Question

if sinx+siny+sinz+sinw=-4 then the value of sin ^400x+sin^300y+sin^200z+sin^100w

Answer 1

We know that ,
f(t) |min = sin (t) |min = -1. ------(1)
That is, minimum value of sin(t) = -1

Here,
$\sin(x) + \sin(y) + \sin(z) + \sin(w) = - 4$

Thus, this is possible,
when,
sin (x) = sin(y) = sin(z) = sin(w) = -1

Therefore,
sin^400(x) + sin^300(y) + sin^200(z) + sin^100(w)
=>
${( - 1)}^{400} + {( - 1)}^{300} + { (- 1)}^{200} \\ + {( - 1)}^{100} \\ = > 1 + 1 + 1 + 1 \\ = > 4$



So, Required value is 4 .