Question

derivation of.......
Sin²theeta + cos² theeta=1

Answer 1

hey friend,,


Let A be the adjacent, O be the opposite and H be the hypotenuses Let A be the adjacent, O be the opposite and H be the hypotenuses

 of a right angle triangle. of a right angle triangle.

cosθ=A/H

sinθ=O/H

Sin^2theeta+Cos^2theeta=(O/H)^2+(A/H)^2
so ,


(A^2+O^2/H^2)

 by Pythagorean Theorem A^2 + O^2 = H^2 

Hence,

Sin^2theeta+Cos^2theeta=1



$thanks$

Jay Hind

Vande mataram_______

Answer 2

Let's take a right angle traingle ABC
so Let's take
$\angle \: a$
$\sin(a) = \frac{p}{h} \\ \cos(a) = \frac{b}{h}$
for angle a perpendicular =AB and base = BC
Hypotenuse = AC
$\sin(a) = \frac{ab}{ac} \\ \sin {}^{2} (a) = \frac{ab^{2} }{ac {}^{2} } \:$
$\cos(a) = \frac{bc}{ac} \\ \cos( a^{2} ) = \frac{ {bc}^{2} }{ {ac}^{2} }$
Now adding both we get
=
$\frac{ {ab}^{2} + {bc}^{2} }{ {ac}^{2} }$
Now by Pythagoras we know ab²+bc²=ac²
so we get
$\frac{ {ac}^{2} }{ {ac}^{2} } = 1$
Sin²+cos²=1