Question

cos 5 theta in terms of cos theta​

Answer 1

Step-by-step explanation:

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Answer 2

Answer: The required expression for cos 5θ in terms of cos

Step-by-step explanation:

The trigonometric function cos (cosine) is periodic with a period of 2π, meaning that it repeats itself every 2π radians. This periodicity can be used to express cos 5θ in terms of cos θ.

Using the angle addition formula for cosine, we can express cos 5θ as:

cos 5θ = cos (4θ + θ)

We can then use the angle addition formula again to expand cos (4θ + θ) as:

cos (4θ + θ) = cos 4θ cos θ - sin 4θ sin θ

Since cos 4θ and sin 4θ can be expressed in terms of cos θ using the multiple angle formulas, we can substitute them in the above equation and simplify to obtain:

cos 5θ = (8 cos³ θ - 4 cos θ) cos θ

Hence, we can express cos 5θ in terms of cos θ as:

cos 5θ = 8 cos⁴ θ - 4 cos² θ

This is the required expression for cos 5θ in terms of cos θ.

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