Question : If $\sec heta+ an heta=5$, then find the value of $ an heta$.
Option 1: $\frac{5}{12}$
Option 2: $\frac{13}{5}$
Option 3: $\frac{13}{3}$
Option 4: $\frac{12}{5}$

Question

Question : If $\sec heta+ an heta=5$, then find the value of $ an heta$.

Option 1: $\frac{5}{12}$

Option 2: $\frac{13}{5}$

Option 3: $\frac{13}{3}$

Option 4: $\frac{12}{5}$

Team Careers360 · Accepted Answer

Correct Answer: $\frac{12}{5}$

Solution : Given: $\sec heta+ an heta=5$--------------------(equation 1)
We know,
$\sec^2 heta- an^2 heta=1$
⇒ $(\sec heta+ an heta)(\sec heta- an heta)=1$
⇒ $(5)(\sec heta- an heta)=1$
⇒ $(\sec heta- an heta)=\frac{1}{5}$----------------------(equation 2)
Now, solving equations 1 and 2 we get,
$ an heta=\frac{12}{5}$
Hence, the correct answer is $\frac{12}{5}$.

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Question : If sec⁡θ+tan⁡θ=5, then find the value of tan⁡θ.Option 1: 512Option 2: 135Option 3: 133Option 4: 125

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Question : If $\sec θ + \tan θ = 5$ , then find the value of $\tan θ$ .
Option 1: $\frac{5}{12}$
Option 2: $\frac{13}{5}$
Option 3: $\frac{13}{3}$
Option 4: $\frac{12}{5}$