Why sin^2(x) + cos^2(x) = 1 ?
perpendicular upon hypotenuse
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,
OP = hypotenuse=1 unit
PB = perpendicular= p (say)
OB= base = b(say)
According to Pythagoras theorem,
p^2 + b^2 = 1^2
Sin^2(x) + Cos^2(x) = 1
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!! 😀
Now, if we divide throughout by sin^2(x)
1+ cot^2(x) = cosec^2(x)
And if we divide throughout by cos^2(x)
tan^2(x) + 1 = sec^2(x)