Question

PROVE sin²θ + cos²θ = 1​

Answer 1

Answer:

Let ABC be a right angled triangle right angled at B.

Let angle C ie angle ACB = theeta.

Now by Pythagoras theorem

AC^2= AB^2+BC^2 ……(1)

We know that sin theeta = opposite side/ hypotenuse.

So sin theeta = AB/AC. Similarly

cos theeta= adjacent side/ hypotenuse

So cos theeta = BC/AC

Now sin^2 theeta + cos^2 theeta

= (AB/AC)^2 + (BC/AC)^2

= AB^2/AC^2 + BC^2/AC^2

= (AB^2+BC^2)/AC^2

= AC^2/AC^2 = 1 ( by using (1) )