Proving The Trigonometric Identity: Sin^2X + Cos^2X = 1 Using The Pythagorean Theorem

sin^2x+cos^2x

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The expression sin^2x + cos^2x is known as the trigonometric identity. This identity states that the sum of the squares of sine and cosine of any angle is always equal to one. This identity holds true for all values of x.

We can prove this identity using the Pythagorean theorem. Consider a right-angled triangle with hypotenuse h, adjacent side a, and opposite side b. By definition, sinx = b/h and cosx = a/h.

Now, using the Pythagorean theorem, we have:

h^2 = a^2 + b^2

Substituting the values of sinx and cosx in terms of a,h and b,h respectively, we get:

h^2 = (h sinx)^2 + (h cosx)^2

Dividing both sides by h^2, we get:

1 = sin^2x + cos^2x

Thus, we have proven the trigonometric identity sin^2x + cos^2x = 1.

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