Question

Prove the above equation

Grade 10- Trigonometry ​

Answer 1

QUESTION:

Prove that cot⁴ A - 1 = cosec⁴ A - 2 cosec² A

GIVEN:

• cot⁴ A - 1 = cosec⁴ A - 2 cosec² A.

TO PROVE:

• cot⁴ A - 1 = cosec⁴ A - 2 cosec² A.

PROOF:

L.H.S: cot⁴ A - 1

$\sf \dashrightarrow (cot^2\ A)^2 -1$

$\boxed{ \bold{ \large{ \green{cosec^2\ \theta - cot^2\ \theta=1}}}}$

$\sf \implies cosec^2\ \theta -1 = cot^2\ \theta$

$\sf \dashrightarrow (cosec^2\ A - 1)^2 -1$

$\boxed{ \bold{ \red{(A - B)^2 = A^2 - 2AB + B^2}}}$

$\sf \dashrightarrow cosec^4\ A - 2\ cosec^2\ A + 1 -1$

$\sf \dashrightarrow cosec^4\ A - 2\ cosec^2\ A$

R.H.S: cosec⁴ A - 2 cosec² A

L.H.S = R.H.S

cot⁴ A - 1 = cosec⁴ A - 2 cosec² A.

HENCE PROVED.

Answer 2

cot⁴A-1 = Cosec⁴A-2Cosec²A

Taking LHS.

Cot⁴A-1

(Cot²A)² - (1)²

(cot²A+1) (cot²A-1)

(Cosec²A-1+1) (Cosec²A-1-1)

(Cosec²A) (Cosec²-2)

Cosec⁴A - 2Cosec². hence proved.

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