**Why sin^2(x) + cos^2(x) = 1 ?**

**Sinx means**

perpendicular upon hypotenuse

**Cosx means**

Base upon hypotenuse

**Let’s take a unit circle,**

A unit circle simply means a circle with radius 1 unit.

It may be 1cm, 1m or any other unit.

Now let’s take a point on this circle, say P.

Now let’s draw a perpendicular from this point on the radius of the circle.

Now we have a triangle OPB,

Where

OP = hypotenuse=1 unit

PB = perpendicular= p (say)

OB= base = b(say)

Now

Sinx= p/1=p

Cosx=b/1=b

**According to Pythagoras theorem,**

p^2 + b^2 = 1^2

So,

Sin^2(x) + Cos^2(x) = 1

Hence,

This is the reason!!

Now, the question arises is what if we don’t take a unit circle?

The answer will be the same, try it yourself!! ðŸ˜€

Now, if we divide throughout by sin^2(x)

We get

1+ cot^2(x) = cosec^2(x)

And if we divide throughout by cos^2(x)

We get

tan^2(x) + 1 = sec^2(x)

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