Answer :

NewStar01

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In Right angle triangle, ∆ABC.. [tex]\sf{\angle B = 90°}[/tex]

By Pythagorus theorem :-

  • AC² = AB² + BC²

Dividing both sides by AC²

  • [tex]\sf{ →\frac{{AC}^{2} }{{AC}^{2} } \: = \frac{{AB}^{2} }{{AC}^{2} } + \frac{{BC}^{2} }{{AC}^{2} } }[/tex]

  • [tex]\sf{ → 1 \: = (\frac{{{AB}^{2} }}{{AC}^{2} }) + (\frac{{BC}^{2} }{{AC}^{2} } ) }[/tex]

  • [tex]\sf{ → 1 \: = { cos }^{2}A + { sin }^{2} A }[/tex]

  • Hence, proved!!

  • sin²∅ + cos²∅ = 1
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