Question

Prove that
1. 1- cos² O = sin² 0.​

Answer 1

Step-by-step explanation:

To prove -

• 1- cos² O = sin² 0

Proof -

• sin²∅ + cos²∅ = 1 (identity)

sin²∅ = 1 - cos²∅ , hence proved

Answer 2

Answer:

Let a, b, c be lengths of right angled triangle

⟼ By definition

$\sinθ = \frac{b}{c} ( \frac{opposite \: side}{hypotenuse} )$

$\cosθ = \frac{a}{c} ( \frac{adjacent \: side}{hypotenuse} )$

$\sin^{2} θ + \cos ^{2} θ = \frac{ {b}^{2} }{ {c}^{2} } + \frac{ {a}^{2} }{ {c}^{2} } = \frac{ {a}^{2} + {b}^{2} }{ {c}^{2} }$

⟼ From Phythagoras theorem

${c}^{2} = {a}^{2} + {b}^{2} \\ \frac{ {a}^{2} + {b}^{2} }{ {c}^{2} } = 1 \\ \sin^{2}θ + \cos^{2}θ = 1 \\ •°• 1 - \cos ^{2} θ = \sin^{2} θ$

⟼ Hence Proved