Question

cos⁴A-sin⁴A=2cos²A-1​

Answer 1

SOLUTION:-

Given:

cos⁴A -sin⁴A = 2cos²A -1

Explanation:

Take L.H.S

cos⁴A -sin⁴A

=) (cos²A)² -(sin²A)²

Here, formula of the a² -b² = (a+b)(a-b)

=) (cos²A +sin²A)(cos²A -sin²A)

=) (1) [cos²A -(1-cos²A)]

=) (cos²A -1 +cos²A)

=) 2cos²A -1 [R.H.S]

Proved.

Answer 2

To prove :-

cos⁴A - sin⁴A = 2 cos²A - 1

Proof :-

LHS

→Cos⁴A - sin⁴A

→(Cos²A)² - (sin²A)²

→As we know that a² - b² = (a+b)(a-b)

→(cos²A + sin²A)(cos²A - sin²A)

→As we know that sin²A + cos²A = 1

→cos²A - sin²A

→Convert sin²A into cos

→cos²A - ( 1- cos²A)

→cos²A - 1 + cos²A

→2 cos²A - 1 = RHS

hence proved

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