Question

verify the identity:
1) tanx^2/secx=sinxtanx
2) cotx^2/cscx=(1-sinx^2)/sinx

Answer 1

1)\[\huge{\frac{(\frac{sinx}{cosx})^2}{\frac{1}{cosx}}}\]\[=\frac{\sin^2x}{cosx}\]\[\huge{=\frac{sinx}{cosx}\times sinx}=tanxsinx\]

Answer 2

same thing for 2
\[\huge{\frac{\cot^2x}{cosecx}}\]\[\huge{=\frac{(\frac{cosx}{sinx})^2}{\frac{1}{sinx}}}\]\[\huge{=\frac{\cos^2x}{sinx}}=\frac{(1-\sin^2x)}{sinx}\]

Answer 3

thank you for clearing this up for me. i forgot that the exponent cancelled out with one of the denominators.

Answer 4

:)