Derive the trig identities cos(2x) = cos²(x) = sin²(x) and sin(2x) = 2 cos(x) sin (x) without using trig identities (Use Euler's Formula)

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A: To evaluate the following integral.

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A: To find the general solution for the equation 1+sin⁡(2x)=sin⁡(x), it can use trigonometric…

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A:

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A: x

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A:

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Q: Making this substitution using [₁ gives us 10 sin²(x) cos³(x) dx 10 10 sin²(x) (1 - sin²(x)) cos(x)…

A: To evaluate the following integral. ∫10 sin2x cos3x dx Note: After seeing the previous solution, we…

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A: Consider the given condition that,2tan (x/2) = (sin2x+1–cos2x)/(sin x(1+cos x)) … (1)Consider the…