Question

The value of $sec^{2}\theta+cosec^{2}\theta$ is equal to

• A. $tan^{2}\theta+cot^{2}\theta$
• B. $sec^{2}\theta\,cosec^{2}\theta$
• C. $sec\theta\,cosec\theta$
• D. $sin^{2}\theta\,cos^{2}\theta$

Answer 1

Answer: (B)

$sec^{2}\theta+cosec^{2}\theta=\frac{1}{cos^{2}\,\theta}+\frac{1}{sin^{2}\,\theta}$
$=\frac{sin^{2}\,\theta+cos^{2}\,\theta}{sin^{2}\,\theta\,cos^{2}\,\theta}$
$=\frac{1}{sin^{2}\,\theta \,cos^{2}\,\theta}$
$=cosec^{2}\,\theta\,sec^{2}\,\theta$