How come $\mathrm{cos}x{\mathrm{tan}}^{2}(x)$ can be changed to $\mathrm{sec}x{\mathrm{sin}}^{2}(x)$ ? What are the steps?

sebadillab0
2022-07-14
Answered

How come $\mathrm{cos}x{\mathrm{tan}}^{2}(x)$ can be changed to $\mathrm{sec}x{\mathrm{sin}}^{2}(x)$ ? What are the steps?

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Where has the other cosine disappeared to?

Then what happens next:

Where has the other cosine disappeared to?

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I need to prove this identity, any idea on how I do it?

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If $\mathrm{tan}\left(\frac{\alpha}{2}\right)=m$ , then evaluate $\frac{1-2{\mathrm{sin}}^{2}\left(\frac{\alpha}{2}\right)}{1+\mathrm{sin}\alpha}$

How to evaluate this?

How to evaluate this?