Question

Please help me!

Answer 1

Answer:

C is correct

Step-by-step 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,

$\sin x=\dfrac{P}{H}$

$\cos x=\dfrac{B}{H}$

Where,

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

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

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

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

$\dfrac{P^2}{H^2}+\dfrac{B^2}{H^2}=1$

$P^2+B^2=H^2$

This is pythagorean Identity

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

Answer 2

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.