Prove that - \sin {}^(2) (\theta) + \cos {}^(2) (\theta) = 1 thankyou ~​

Question

Prove that -


`\sin {}^(2) (\theta) + \cos {}^(2) (\theta) = 1`


thankyou ~​

Answer 1

Step-by-step explanation:

In the right triangle shown in the attachment, we have, by definition, ...

sin(θ) = a/c

cos(θ) = b/c

Then ...

sin²(θ) +cos²(θ) = (a/c)² +(b/c)² = (a² +b²)/c²

By the Pythagorean theorem, ...

c² = a² +b²

Substituting for c², we have ...

sin²(θ) +cos²(θ) = (a² +b²)/(a² +b²)

sin²(θ) +cos²(θ) = 1

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Additional comment

This trig identity also goes by the name "Pythagorean identity."