Question

sin² 45⁰+cos² 45⁰ =1 (proved that)​

Answer 1

answer in the attachment.

Answer 2

△ ABC is a right-angled triangle.

BC=AB=a

$From \: the \: Pythagoras \: Theorem ,\: we \: get$

AC²=AB²+BC²

Or, AC²=a²+a²

Or, AC²=2a²

$or \: AC = \sqrt{2 {a}^{2} } \\ or \: AC= \sqrt{2} a$

$Now \\ \sin \: 45⁰= \frac{AB}{AC} = \frac{a}{ \sqrt{2} a} = \frac{1}{ \sqrt{2} }$

$\cos \: 45⁰= \frac{BC}{AC} = \frac{a}{ \sqrt{2a} } = \frac{1}{ \sqrt{2} }$

Now,

${ \sin^2} 45⁰+ { \cos} \: ^{2} 45⁰\\ = \frac{1}{ \sqrt{2} } + \frac{1}{ \sqrt{2} } \\ = \frac{1 + 1}{2} \\ = \frac{2}{2} \\ = 1 \:[ Proved]$

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