JIPMAT 2022 (QA) - Given below are two statement: Statement I: If ()=5/13, then the value of ()=5/12 Statement II: if ()=12/5, then the value of ()=5/12 In the light of the above statements, choose the correct answer form the question below: | PYQs + Solutions

JIPMAT 2022

Geometry

Trigonometry

Easy

Given below are two statement:
Statement I: If $\sin (\theta)=\frac{5}{13}$ , then the value of $\tan (\theta)=\frac{5}{12}$
Statement II: if $\cot (\theta)=\frac{12}{5}$ , then the value of $\sin (\theta)=\frac{5}{12}$
In the light of the above statements, choose the correct answer form the question below:

Both Statement I and Statement II are true

Both Statement I and Statement II are false

Statement I is true but Statement II is false

Statement I is false but Statement II is true

✅ Correct Option: 3

Statement I: If

\sin(\theta) = \frac{5}{13}

In right triangle:

\sin^2(\theta) + \cos^2(\theta) = 1

(\frac{5}{13})^2 + \cos^2(\theta) = 1

\cos^2(\theta) = 1 - \frac{25}{169} = \frac{144}{169}

\cos(\theta) = \frac{12}{13}

Therefore

\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)} = \frac{5}{13} × \frac{13}{12} = \frac{5}{12}

✓

Statement II: If

\cot(\theta) = \frac{12}{5}

\cot(\theta) = \frac{\cos(\theta)}{\sin(\theta)} = \frac{12}{5}

Therefore

\sin(\theta) = \frac{5}{13}

(using

\sin^2(\theta) + \cos^2(\theta) = 1

again)

\newline

Not equal to

\frac{5}{12}

✗

Therefore, Statement I is true and Statement II is false.