Question

How do you prove `Sinx+cosx=1`?

Answer 1

it is `sin^2x+cos^2 x` which is equal to 1!

Explanation:

Just imagine any rectangle triangle. Take one of its acute angles.

The sine of this angle is the opposite catet dividing by the hypotenuse (a/h), and the cosins of this angle is the adjacent catet dividing by the hypotenuse (b/h)

So

`sin^2x+cos^2 x=(a/h)^2+(b/h)^2= (a^2+b^2)/(h^2)`

But by the Pythagoras theorem we know that the sum of the square of the catets `(a^2+b^2)` it is the square of the hypotenuse:

So `(a^2+b^2)/(h^2)=(h^2)/(h^2)=1`