Question

prove sin^2+cos^2=1​

Answer 1

Answer:

Let there be a ΔABC right angled at B. Then, AC is the hypotenuse.

Let AB be the base and BC be the perpendicular. Let ∠A=θ

sinθ=perpendicular/hypotenuse

     =BC/AC

cosθ=base/hypotenuse

       =AB/AC

sin²θ+cos²θ=(BC²+AB²)/AC²

                   =AC²/AC²             [AB²+BC²=AC²;Pythagoras theorem]

                   =1

HENCE PROVED.

Answer 2

Step-by-step explanation:

sin^2 theta + cos^2 theta =1

as we know that

sin theta=opp side/hyp

cos theta=adj side / hyp

then,opp side^2/hyp^2+adj side^2/hyp^2

=opp side ^2 +adj side^2 / hyp^2

=hyp^2/hyp^2=1