Learn Prove That Sin6 X Cos6 X 1 3 Sin2cos2 X
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Prove that: sin6 x + cos6 x = 1 - 3 sin2 x cos2 x.
Cosine and Sine are primary trigonometric functions. They are also known as complemetary functions
Answer: sin6 x + cos6 x = 1 - 3 sin2 x cos2 x
To solve this, we will use algebraic identity.
Explanation:
sin6 x + cos6 x can be written as (sin2x )3 + (cos2x )3
Using Algebraic identity,
a3 + b3 = (a + b)3 - 3ab (a + b)
(sin2x )3 + (cos2x )3 = (sin2x + cos2x )3 - 3 sin2x cos2x (sin2x + cos2x )
Using trigonometric identity sin2x + cos2x = 1, we get
⇒ sin6 x + cos6 x = (1) 3 - 3 sin2x cos2x (1)
⇒ sin6 x + cos6 x = 1 - 3 sin2x cos2x
Thus, proved that sin6 x + cos6 x = 1 - 3 sin2 x cos2 x
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