Question:-V3 and cosec 0 = 2, without using a calculator, calculatethe value of sec20 + tan20answer :3

Consider the provided question, Given, cotθ=-3 and cosecθ=2 We have to find the value of…

Answered: -V3 and cosec 0 = 2, without using a…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.2: Trigonometric Functions Of Angles

Problem 18E

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Step 1

Consider the provided question,

$G i v e n, \cot θ = - \sqrt{3} a n d \cos e c θ = 2$

We have to find the value of $\sec^{2} θ + \tan^{2} θ$ .

$S i n c e, \cot θ = - \sqrt{3} W e k n o w t h a t, \tan θ = \frac{1}{\cot θ} \Rightarrow \tan θ = - \frac{1}{\sqrt{3}}$

Step 2

$G i v e n, \cot θ = - \sqrt{3} a n d \cos e c θ = 2 D i v i d e \cos e c θ b y \cot θ . \Rightarrow \frac{\cos e c θ}{\cot θ} = \frac{2}{- \sqrt{3}} \Rightarrow \frac{\frac{1}{\sin θ}}{\frac{\cos θ}{\sin θ}} = \frac{2}{- \sqrt{3}} [U s e, \cos e c θ = \frac{1}{\sin θ}, \cot θ = \frac{\cos θ}{\sin θ}] \Rightarrow \frac{1}{\cos θ} = \frac{2}{- \sqrt{3}} \Rightarrow \sec θ = - \frac{2}{\sqrt{3}} [U s e \sec θ = \frac{1}{\cos θ}]$

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