Post History
#2: Post edited
by
Wolgwang
·
2021-08-07T07:57:51Z (over 3 years ago)
Format improved
- Simplifying $LHS$:
<p>$$\displaylines{(\cos^3\theta+\sin^3\theta)^2\\=\cos^6\theta+\sin^6\theta+2\cos^3\theta\sin^3\theta\\=\cos^6\theta\bigg(1+\dfrac{\sin^6\theta}{\cos^6\theta}+2\dfrac{\cos^3\theta\sin^3\theta}{\cos^6\theta}\bigg)\\=\cos^6\theta(1+\tan^6\theta+2\tan^3\theta)\\=\cos^6\theta[1^2+(\tan^3\theta)^2+2(1)(\tan^3\theta)]\\=\cos^6\theta(1+\tan^3\theta)^2\\=RHS}$$</p>- Hence proved.
- Simplifying $LHS$:
- <p>
- \begin{align}
- (\cos^3\theta+\sin^3\theta)^2&=\cos^6\theta+\sin^6\theta+2\cos^3\theta\sin^3\theta\\&=\cos^6\theta\bigg(1+\dfrac{\sin^6\theta}{\cos^6\theta}+2\dfrac{\cos^3\theta\sin^3\theta}{\cos^6\theta}\bigg)\\&=\cos^6\theta(1+\tan^6\theta+2\tan^3\theta)\\&=\cos^6\theta[1^2+(\tan^3\theta)^2+2(1)(\tan^3\theta)]\\&=\cos^6\theta(1+\tan^3\theta)^2\\&=RHS
- \end{align}
- Hence proved.
#1: Initial revision
by
Wolgwang
·
2021-08-07T07:53:39Z (over 3 years ago)
Simplifying $LHS$:
<p>$$\displaylines{(\cos^3\theta+\sin^3\theta)^2\\=\cos^6\theta+\sin^6\theta+2\cos^3\theta\sin^3\theta\\=\cos^6\theta\bigg(1+\dfrac{\sin^6\theta}{\cos^6\theta}+2\dfrac{\cos^3\theta\sin^3\theta}{\cos^6\theta}\bigg)\\=\cos^6\theta(1+\tan^6\theta+2\tan^3\theta)\\=\cos^6\theta[1^2+(\tan^3\theta)^2+2(1)(\tan^3\theta)]\\=\cos^6\theta(1+\tan^3\theta)^2\\=RHS}$$</p>
Hence proved.