Trigonometric identities

Prove the identity 1-cos^{2}x= cos^{2 }x tan^{2 }x

Hint: use t-chart

Left hand side right hand side

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- December 28th 2012, 11:45 AMalejandroTrigonometric identities
**Trigonometric identities**

Prove the identity 1-cos^{2}x= cos^{2 }x tan^{2 }x

Hint: use t-chart

Left hand side right hand side - December 28th 2012, 11:50 AMabenderRe: Trigonometric identities
Attempt?

- December 28th 2012, 12:47 PMzachd77Re: Trigonometric identities
The LHS side reduces to sin^2(x), due to the LHS being an offshoot of the Pythagorean Identity sin^2(x)+cos^2(x)=1. The RHS side can be rewritten as cos^2(x)*(sin^2(x)/cos^2(x)), due to the fact that the definition of the tangent ratio is the sine of the angle over the cosine of the angle. The cos^2(x) cancels out, leaving sin^2(x). Since both sides are equal (without crossing the equal sign), the identity has been proven.