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Please help me!
Which of the following options is a Pythagorean Identity?

A. (sin(x) - cos(x))^2 = 1 + 2sin(x)cos(x)
B. (sin(x) - cos (x))^2 = 1
C. (sin(x) - cos (x))^2 = 1 - 2sin(x)cos(x)
D. sin^2(x) - cos^2(x) = 1

Respuesta :

cdw2014
The answer is D. Think of the Pythagorean Theorem which states that a^2 + b^2 = c^2. The Pythagorean Identities used in trigonometry are the angle version which can be used to simplify expressions.
isyllus

Answer:

C is correct

Step-by-step explanation:

We need to choose Pythagoreon Identity

[tex](\sin x-\cos x)^2=1-2\sin x\cos x[/tex]

[tex](a-b)^2=a^2+b^2-2ab[/tex]

[tex]\sin^2 x+\cos^2 x-2\sin x\cos x=1-2\sin x\cos x[/tex]

Cancel line term from both sides

[tex]\sin^2x+\cos^2x=1[/tex]

As we know,

[tex]\sin x=\dfrac{P}{H}[/tex]

[tex]\cos x=\dfrac{B}{H}[/tex]

Where,

[tex]P\rightarrow \text{ Perpendicular of Right triangle}[/tex]

[tex]B\rightarrow \text{ Base of Right triangle}[/tex]

[tex]H\rightarrow \text{ Hypotenuse of Right triangle}[/tex]

[tex]\sin^2x+\cos^2x=1[/tex]

[tex]\dfrac{P^2}{H^2}+\dfrac{B^2}{H^2}=1[/tex]

[tex]P^2+B^2=H^2[/tex]

This is pythagorean Identity

Hence, [tex](\sin x-\cos x)^2=1-2\sin x\cos x[/tex] this is pythagorean identity