Question

(sin^4Q - cos^4Q + 1) cosec^2Q = 2

Answer 1

||✪✪ QUESTION ✪✪||

Prove that (sin^4A -cos^4A +1)cosec^2A = 2 . ?

|| ✰✰ ANSWER ✰✰ ||

Taking LHS, we get,

→ (sin⁴A- cos⁴A + 1)cosec²A

→ [(sin²A)²-(cos²A)² + 1)cosec²A

using (a² - b²) = (a+b)(a-b) now,

→ [ (sin²A+cos²A)(sin²A-cos²A) + 1]cosec²A

Putting Sin²A + cos²A = 1 now,

→ (sin²A - cos²A + 1)cosec²A

→ [ sin²A + (1 - cos²A) ]cosec²A

Putting (1 - cos²A) = sin²A now,

→ [ sin²A + sin²A ] cosec²A

→ 2sin²A * cosec²A

Putting cosecA = 1/sinA now,

→ 2 * sin²A * 1/sin²A

→ 2 = RHS.

✪✪ Hence Proved ✪✪

Answer 2

Step-by-step explanation:

$\huge\underline\purple{\sf Answer :-}$

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