Trigonometric Identity

MathematicsTrigonometryEasy

Published: May 3, 2026

Question

$$sin^{2}\alpha + cos^{2}\alpha = 1$$

Animated Video Solution

The first half plays free, the full solution is in the app.

Step 1

Hi Sarvar, let's explore one of the most fundamental identities in trigonometry: why sine squared alpha plus cosine squared alpha equals one.

Step 2

To understand this, let's visualize a right-angled triangle with an angle alpha.

Step 3

Recall the definitions of sine and cosine based on the sides of this triangle.

\sin(\alpha) = \frac{y}{r}

\cos(\alpha) = \frac{x}{r}

Step 4

If we square these ratios and add them together, we get the expression from our original problem.

\sin^2(\alpha) + \cos^2(\alpha) = \left(\frac{y}{r}\right)^2 + \left(\frac{x}{r}\right)^2

Step 5

By expanding the squares, we can rewrite this as y squared plus x squared, all over r squared.

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