Question

prove that
${cosec}^{4} a \: - \: 2 {cosec}^{2} a + 1 = \\ {cot}^{4} a$
pls help
answer properly for Brainliest​

Answer 1

Step-by-step explanation:

cosec⁴a - 2Cosec²a +1 =cot⁴a

L.H.S

cosec⁴a - 2Cosec²a +1

(1+cot²a)²-2(1+cot²a)+1

1+cot⁴a+2cot²a-2-2cot²a+1

cot⁴a

R.H.S

Answer 2

Answer:

Proved

Step-by-step explanation:

$\text{cosec}^4a-2\text{cosec}^2a+1=(\text{cosec}^2a)^2-2\times(\text{cosec}^2a)\times1+(1)^2\\=((\text{cosec}^2a)-1)^2\\=(\text{cot}^2a)^2 \text{ (since cosec}^2-1=\text{cot}^2a)}\\=\text{cot}^4a$