Question

Find the values of trigonometric ratios and the value of θ.​

Answer 1

Step-by-step explanation:

tan θ = 2 …[Given]

We know that, 1 + tan2 θ = sec7 θ

∴ 1 + (2)7 = sec7 θ

∴ 1 + 4 = sec7 θ

∴ sec7 θ = 5

∴ sec θ = √5 …

[Taking square root of both sides]

Answer 2

Given,

Find the values of trigonometric ratios and the value of θ.​

Solution,

Know that the trigonometric ratios are as follows

$\[\begin{array}{l} \Rightarrow \sin \theta = \frac{{{\rm{Perpendicular}}}}{{{\rm{Hypotenuse}}}};\cos ec\theta = \frac{1}{{\sin \theta }}\\ \Rightarrow \cos \theta = \frac{{{\rm{Base}}}}{{{\rm{Hypotenuse}}}};sec\theta = \frac{1}{{\cos \theta }}\\ \Rightarrow \tan \theta = \frac{{{\rm{Perpendicular}}}}{{{\rm{Base}}}};\cot \theta = \frac{1}{{\tan \theta }}\end{array}\]$

The values  $\[\theta \]$ are as follows