I have no idea why I imagine that I couldn't , but I frankly face that problem, I know there's identity sin^2(x) + cos^2(x) = 1 , but ! while solving like if I have another problem like

Sin(x)^2 + Cos(x)^2 = X^2+Y^2+Z^2 .. so here i STUCK although I know that there's

sin^2(x) + cos^2(x) = 1 but the question why I could assign that?! here what's exactly I'm facing while solving question ...

maybe because sin^2(x) + cos^2(x) = 1 it's not given explicitly like sin^2(x) + cos^2(x) = 1 ..... so I get mislead while it's given with other equation like Sin(x)^2 + Cos(x)^2 = X^2+Y^2+Z^2....how can I solve that problem of thinking ?!!

Again, you make up some problem to confuse yourself.

expression one = expression two.

All that means is that the two expressions represent the same numeric value.

\(\displaystyle cos^2(x) + sin^2(x) = \text {some expression.}\)

But no matter what x is \(\displaystyle cos^2(x) + sin^2(x) = 1.\)

So \(\displaystyle cos^2(x) + sin^2(x)\) and 1 are just different names for the exact same numeric value.

And because

**you** have

**stipulated** that \(\displaystyle cos^2(x) + sin^2(x) = \text {some expression.}\),

then some expression is just a third name for the exact same numeric value, namely 1.

The equal sign simply means "has the same numeric value."

You asked this exact same question using x, y, and z weeks ago.

Here is a

**BASIC** rule of algebra: \(\displaystyle x = y \text { and } y = z \implies x = z.\)

Learn it and move on.