Answered

Discover a wealth of knowledge at Westonci.ca, where experts provide answers to your most pressing questions. Explore thousands of questions and answers from knowledgeable experts in various fields on our Q&A platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

13. Which of the following is not a correct relation?

A. sin ⁡ 2 = 1 − cos ⁡ 2 sin 2 θ=1−cos 2 θ

B. sec ⁡ 2 = 1 + tan ⁡ 2 sec 2 θ=1+tan 2 θ

C. cosec ⁡ 2 = 1 + cot ⁡ 2 cosec 2 θ=1+cot 2 θ

D. sec ⁡ 2 = 1 − tan ⁡ 2 sec 2 θ=1−tan 2 θ​

13 Which Of The Following Is Not A Correct Relation A Sin 2 1 Cos 2 Sin 2 Θ1cos 2 Θ B Sec 2 1 Tan 2 Sec 2 Θ1tan 2 Θ C Cosec 2 1 Cot 2 Cosec 2 Θ1cot 2 ΘD Sec 2 1 class=

Sagot :

answer of this question is

option (B)

semsee45

Answer:

[tex]\textsf{D)}\quad \sec^2\theta=1-\tan^2\theta[/tex]

Step-by-step explanation:

To determine which of the given equations is not a correction relation, we can use the Pythagorean Identity, sin²θ + cos²θ = 1.

[tex]\dotfill[/tex]

Option A

If we subtract cos²θ from both sides of the Pythagorean Identity, we get:

[tex]\sin^2\theta +\cos^2\theta-\cos^2\theta= 1- \cos^2\theta \\\\ \sin^2\theta = 1- \cos^2\theta[/tex]

Therefore, sin²θ = 1 - cos²θ is a correct relation.

[tex]\dotfill[/tex]

Option B

Divide both sides of the Pythagorean Identity by cos²θ:

[tex]\dfrac{\sin^2\theta}{\cos^2\theta} +\dfrac{\cos^2\theta}{\cos^2\theta} =\dfrac{1}{\cos^2\theta} \\\\\\ \tan^2\theta+1=\sec^2\theta[/tex]

Switch sides:

[tex]\sec^2\theta=1 + \tan^2\theta[/tex]

Therefore, sec²θ = 1 + tan²θ is a correct relation.

[tex]\dotfill[/tex]

Option C

Divide both sides of the Pythagorean Identity by sin²θ:

[tex]\dfrac{\sin^2\theta}{\sin^2\theta} +\dfrac{\cos^2\theta}{\sin^2\theta} =\dfrac{1}{\sin^2\theta} \\\\\\ 1+\cot^2\theta=\text{cosec}^2\theta[/tex]

Switch sides:

[tex]\text{cosec}^2\theta=1 + \cot^2\theta[/tex]

Therefore, cosec²θ = 1 + cot²θ is a correct relation.

[tex]\dotfill[/tex]

Option D

Divide both sides of the Pythagorean Identity by cos²θ:

[tex]\dfrac{\sin^2\theta}{\cos^2\theta} +\dfrac{\cos^2\theta}{\cos^2\theta} =\dfrac{1}{\cos^2\theta} \\\\\\ \tan^2\theta+1=\sec^2\theta[/tex]

Switch sides:

[tex]\sec^2\theta=1 + \tan^2\theta[/tex]

Therefore, sec²θ = 1 - tan²θ is NOT a correct relation.

Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.