Practicing Success
What is the value of $\left(\frac{1+sec^2A}{1+cos^2A}\right)\left(\frac{1+sin^2A}{1+cosec^2A}\right)$? |
$cos^2A$ $cosex^2A$ $sec^2A$ $tan^2A$ |
$tan^2A$ |
$\left(\frac{1+sec^2A}{1+cos^2A}\right)\left(\frac{1+sin^2A}{1+cosec^2A}\right)$ Put A = 45° = $\frac{1+2}{1+\frac{1}{2}}.\frac{1+\frac{1}{2}}{1+2}$ = 1 This is true for option 3 and 4 Solving, $\left(\frac{1+sec^2A}{1+cos^2A}\right)\left(\frac{1+sin^2A}{1+cosec^2A}\right)$ = $\frac{1+\frac{1}{cos^2A}}{1+cos^2A}.\frac{1+sin^2A}{1+\frac{1}{sin^2A}}$ = $\frac{sin^2A}{cos^2A}$ = tan²A
|