Question

Prove that sin²θ + cos²θ = 1​

Answer 1

Step-by-step explanation:

Let (C) be a unit circle, and M∈(C). Also, we will denote ∠IOM as θ (see the diagram). From the unit circle definition, the coordinates of the point M are (cosθ,sinθ).

And so, OC¯¯¯¯¯¯¯¯ is cosθ

and OS¯¯¯¯¯¯¯ is sinθ.

Therefore, OM=OC¯¯¯¯¯¯¯¯2+OS¯¯¯¯¯¯¯2

−−−−−−−−−

√=cos2θ+sin2θ−−−−−−−−−−−

√. Since M lies in the unit circle, OM is the radius of that circle, and by definition, this radius is equal to 1. It immediately follows

sin²θ + cos²θ = 1

Answer 2

Step-by-step explanation:

sinθ = P/H ---------------1

cosθ = B/H --------------2

Now , LHS

sin²θ + cos²θ

from 1 and 2

$p {}^{2} \div h {}^{2} + b {}^{2} \div h {}^{2} \\ p { }^{2} + b {}^{2} \div h {}^{2} \\ h {}^{2} \div h {}^{2} \\ = 1$

By Pythagoras theorem

P² + B² = H²

LHS = RHS

HENCE PROVED