prove sinx^2+cosx^2=1, graphically.

1. Case(1) x is an acute angle.
   In triangle ABC, let B be a right angle, x be the measure of angle A, AB = c, BC = a, CA = b.
   Then sin x = a/b, cos x = c/b.
   sin^2 x + cos^2 x = a^2/b^2 + c^2/b^2 =(a^2+c^2)\b^2= b^2/b^2 = 1, by Pythagoras theorem.
2. Case(2) x is any angle.
   An angle whose initial side coincides with OX, in the xy-plane, is said to be in the standard position. The circle with center at the origin and radius 1, is called the unit circle.
   Let x be the measure of an angle (in the positive or negative direction) in the standard position. Suppose its terminal side cuts the unit circle at P. Then (cos x, sin x) are the coordinates of P. Since P is on the unit circle,
   cos^2 x + sin^2 x = 1.

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Rinkoo Gupta

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