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Trigonometric identities Calculator

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Example
Created on 2024-06-20Asked by Jack Carter (Solvelet student)
Verify the identity sin⁡2(x)+cos⁡2(x)=1\sin^2(x) + \cos^2(x) = 1.

Solution

To verify the identity sin⁡2(x)+cos⁡2(x)=1\sin^2(x) + \cos^2(x) = 1: 1. **Pythagorean identity:** sin⁡2(x)+cos⁡2(x)=1. \sin^2(x) + \cos^2(x) = 1. 2. **Using the unit circle:** - On the unit circle, any point (cos⁡(x),sin⁡(x))(\cos(x), \sin(x)) lies on the circle defined by x2+y2=1x^2 + y^2 = 1. - Therefore, cos⁡2(x)+sin⁡2(x)=1\cos^2(x) + \sin^2(x) = 1. 3. **Result:** The identity sin⁡2(x)+cos⁡2(x)=1\sin^2(x) + \cos^2(x) = 1 is verified. Solved on Solvelet with Basic AI Model
Some of the related questions asked by Avery Lewis on Solvelet
1. Prove the identity cos⁡2(x)+sin⁡2(x)=1\cos^2(x) + \sin^2(x) = 1 for all values of xx.2. Simplify the expression tan⁡(x)1−cot⁡(x) \frac{\tan(x)}{1 - \cot(x)} .,
DefinitionTrigonometric identities are equations that hold for every value of a variable in the domain where the function is defined. The Pythagorean identity sin2(x)+cos2(x)=1 holds for all x.
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