Question

if root 5 tan theta is equal to 1 find sec square theta minus sin square theta divided by cos square theta + sec square theta​

Answer 1

Step-by-step explanation:

cos2θ+sec2θcosec2θ−sec2θ=61144

Step-by-step explanation:

Given:

tan\theta=\frac{1}{\sqrt5}tanθ=51

\implies\:cot\theta=\sqrt5⟹cotθ=5

sec^2\theta=1+tan^2\thetasec2θ=1+tan2θ

sec^2\theta=1+\frac{1}{5}sec2θ=1+51

sec^2\theta=\frac{6}{5}sec2θ=56

\implies\:cos^2\theta=\frac{5}{6}⟹cos2θ=65

Now,

\frac{cosec^2\theta-sec^2\theta}{cos^2\theta+sec^2\theta}cos2θ+sec2θcosec2θ−sec2θ

=\frac{(1+cot^2\theta)-(1+tan^2\theta)}{cos^2\theta+sec^2\theta}=cos2θ+sec2θ(1+cot2θ)−(1+tan2θ)

=\frac{cot^2\theta-tan^2\theta}{cos^2\theta+sec^2\theta}=cos2θ+sec2θcot2θ−tan2θ

=\frac{5-\frac{1}{5}}{\frac{5}{6}+\frac{6}{5}}=65+565−51

=\frac{\frac{25-1}{5}}{\frac{25+36}{30}}=3025+36525−1

=\frac{\frac{24}{5}}{\frac{61}{30}}=3061524

=\

Answer 2

Answer:

........hope it's helpful for you