Answer to Question #100446 in Trigonometry for Gaby

Question

Verify: csc⁴x-2csc²x+1=cot⁴x

Answer 1

We need to verify $csc^4 x - 2 csc^2 x + 1 = cot^4 x$

We know $a^2 - 2a + 1 = (a - 1)^2$ and

$a^4 - 2 a^2 + 1 = (a^2 -1)^2$

$csc^2 x - 1 = cot^2 x$

Now,

apply the above formula for this Question

$$csc^4 x - 2 csc^2 x + 1 = (csc^2 - 1) ^2$$

$$=(cot^2 x)^2 = cot^4 x$$

Answer: Yes, it was proved that

$$csc^4 x - 2 csc^2 x + 1 = cot^4 x$$