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Multiplication of Matrices

cos 4 A -sin ...

Question

cos⁴A - sin⁴A +1=.

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Solution

Cos⁴A - Sin⁴A =
(Cos²A - Sin²A)(Cos²A + Sin²A)

We know that
Cos²A + Sin²A=1
Therefore
Cos⁴A - Sin⁴A =Cos²A - Sin²A=cos 2A

Therefore We know that cos2A= 2Cos²A - 1
Therefore

Cos⁴A - Sin⁴A = 2Cos²A - 1

Hence

Cos⁴A - Sin⁴A +1 = 2Cos²A -

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Similar questions

{cos}^{4} A - {sin}^{4} A + 1 - 2 {cos}^{2} A

{cos}^{4} A - {sin}^{4} A + 1 = 2 {cos}^{2} A .

Q. Prove that :

{sin}^{4} A + {cos}^{4} A = 1 - 2 {sin}^{2} A {cos}^{2} A

Q. If sin⁴ A – cos⁴ A = 1 and 0 < A ≤ 90°, then A = __________.

{sin}^{4} A + {cos}^{4} A = 1 - 2 {sin}^{2} A \cdot {cos}^{2} A

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