What is the value of $\left(\frac{1+sec^2A}{1+cos^2A}\right)\left(\frac{1+sin^2A}{1+cosec^2A}\right)$?
Answer & explanation
Correct answer: option 4
$\left(\frac{1+sec^2A}{1+cos^2A}\right)\left(\frac{1+sin^2A}{1+cosec^2A}\right)$
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