(tan α + cot α)²=sec²α+cosec²α Cara pembuktian identitas trigonometri

[tex] {( \frac{ \sin( \alpha ) }{ \cos( \alpha ) } + \frac{ \cos( \alpha ) }{ \sin( \alpha ) } )}^{2} = {( \frac{ {sin}^{2} \alpha + {cos}^{2} \alpha }{ \sin( \alpha ) \cos( \alpha ) })}^{2} = \frac{1}{ {sin}^{2} \alpha \times {cos}^{2} \alpha } = \\ \frac{ {sin}^{2} \alpha + {cos}^{2} \alpha }{ {sin}^{2} \alpha \times {cos}^{2} \alpha } = \frac{1}{ {cos}^{2} \alpha } + \frac{1}{ {sin}^{2} \alpha } = {sec}^{2} \alpha + {cosec}^{2} \alpha [/tex]