Question

sin theta * sin theta + cos theta * cos theta = 1 prove it

Answer 1

sin theta*sin theta + cos theta*cos theta
sin^2 theta+cos^2theta
and by the identity = sin^2theta+cos^2theta=1
we can get the proving part that is 1

Answer 2

Lets take a right angled triangle having sides 1 and 1.

Let a and b are the two sides.

So the third side, using Pythagorus Theorem,

c² = a² + b² = 1² + 1² = 2

c = √2 units


Let theta be an angle (other than the right angle) in the triangle...

sine theta = opp/hyp = 1 /√2

So, sine² theta = 1/2

cosine² theta = adj/hyp = 1 /√2

So, cosine² theta = 1/2


Therefore,

sine² theta + cosine² theta = (1/2) + (1/2) = 1.

Hence, proved.

-WonderGirl