Question

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

Answer 1

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.

Answer 2

C is correct

Explanation:

We need to choose Pythagoreon Identity

`(\sin x-\cos x)^2=1-2\sin x\cos x`

`(a-b)^2=a^2+b^2-2ab`

`\sin^2 x+\cos^2 x-2\sin x\cos x=1-2\sin x\cos x`

Cancel line term from both sides

`\sin^2x+\cos^2x=1`

As we know,

`\sin x=(P)/(H)`

`\cos x=(B)/(H)`

Where,

`P\rightarrow \text{ Perpendicular of Right triangle}`

`B\rightarrow \text{ Base of Right triangle}`

`H\rightarrow \text{ Hypotenuse of Right triangle}`

`\sin^2x+\cos^2x=1`

`(P^2)/(H^2)+(B^2)/(H^2)=1`

`P^2+B^2=H^2`

This is pythagorean Identity

Hence,
`(\sin x-\cos x)^2=1-2\sin x\cos x` this is pythagorean identity