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How do you prove cos4 (x) - sin4 (x) = cos (2x)?
sin(θ) is the ratio of the opposite (base) side to the hypotenuse, while cos(θ) is the ratio of the adjacent (perpendicular) side to the hypotenuse.
Answer: Hence proved that cos4 (x) - sin4 (x) = cos (2x)
Let's solve step by step using trigonometric identities.
We will start from LHS
(cos2 x)2 - (sin2 x)2
By using the property, a2 - b2 = (a + b) (a - b)
(cos2 x)2 - (sin2 x)2 = (cos2 x + sin2 x) (cos2 x - sin2 x)
= (1) × cos 2x, by using the trigonometric identities
= cos 2x = RHS
So, LHS = RHS
Hence, it is proved that cos4 (x) - sin4 (x) = cos (2x)