Question

give that tan theta is equal to 1/under root 5

what is the value of the cosec squared theta minus sec squared theta cosec squared theta + sec squared theta

Answer 1

Next steps are:

=(30-6/5 × 30+6/5)
=(24/5 × 36/5)
=(864/25)
=34.56

Answer 2

Answer:

The value of the given expression is 34.56

Step-by-step explanation:

$\tan\theta=\frac{1}{\sqrt{5}}\implies \cot\theta=\frac{1}{\tan\theta} \implies\cot\theta=\sqrt{5}\\\\\csc^2\theta=1+\cot^2\theta\\\\\csc^2\theta=1+(\sqrt{5})^2\\\\\implies\csc^2\theta=6 \\\\\sec^2\theta=1+\tan^2 \theta \\\implies \sec^2\theta=1+(\frac{1}{\sqrt{5}})^2\\\\\implies\sec^2 \theta=\frac{5}{6}$

now, to find : (csc²θ - sec²θ)·(csc²θ + sec²θ)

$=\csc^4\theta-\sec^4\theta\\=(\csc^2\theta)^2-(\sec^2\theta)^2\\\\=(6)^2-(\frac{6}{5})^2\\\\=36-\frac{36}{25}\\\\=\frac{864}{25}\\\\=34.56$

Hence, The value of the given expression is 34.56