Question

sin squared theta + cos squared theta equals to 1

Answer 1

hey friend your answer is
it is the formula sin^2theta+cos^2 theta =1

Answer 2

It depends on which definition we use. If we use the unit circle, then the definition includes this phrase so I call the unit circle variant done.

Let’s get to the normal triangle thing. Then sinx=acsin⁡x=ac and cosx=bccos⁡x=bc. Then sin2x+cos2x=a2+b2c2sin2⁡x+cos2⁡x=a2+b2c2, which is indeed 1 (by the Pythagorean identity; c is the hypotenuse).

The differential variant actually is harder (and I don’t yet have the formal tools to prove it this way, although it’s definitely of genuine interest to me: exploring differential equations and consequences of the definition as solution to the equation)
hope it will help you ✨✌️✨✌️✨✌️