I have an assignment question that says "Express $\sin 4\theta$ by formulae involving $\sin$ and $\cos$ and its powers." I'm told that $\sin 2\theta = 2 \sin\theta \cos\theta$ but I don't know how this was found.

Factor 2 2 out of 4θ 4 θ. sin(2(2θ)) sin (2 (2 θ)) Apply the sine double - angle identity. 2(2sin(θ)cos(θ))cos(2θ) 2 (2 sin (θ) cos (θ)) cos (2 θ) Multiply 2 2 by 2 2. 4(sin(θ)cos(θ))cos(2θ) 4 (sin (θ) cos (θ)) cos (2 θ) Use the double - angle identity to transform cos(2x) cos (2 x) to 2cos2(x)−1 2 cos 2 (x) - 1.

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Jan 12, 2023 · I want to write $\sin(4\theta)$ in terms of $\cos(\theta)$ and $\sin(\theta)$. My work: \begin{align*}\sin(4\theta) & = 2\sin(2\theta) \cos(2\theta) \\ &= 2[(2\sin(\theta) \cos(\theta)(2\c...

Need help using De Moivre's theorem to write \cos 4\theta & \sin 4\theta as terms of \sin\theta and \cos\theta

In trigonometry formulas, we will learn all the basic formulas based on trigonometry ratios (sin,cos, tan) and identities as per Class 10, 11 and 12 syllabi. Also, find the downloadable PDF of trigonometric formulas at BYJU'S.

Folks, how can $\sin^4(x)$ be simplified to a trig function with power of 1? I tried: $(\sin^2(x))^2 = ((1-\cos2x)/2)^2$ but still getting $\cos x$ to the power of $2$. Wolframalpha only shows the ...

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