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
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.