Question

If sec θ = 41/9 then tan θ = ? *​

Answer 1

40 / 9 is the required answer

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Answer 2

Answer:

Step-by-step explanation:

We have,

$\tt{sec(\theta)=\dfrac{41}{9}}$

$\tt{\implies\,sec^2(\theta)=\dfrac{(41)^2}{(9)^2}}$

$\tt{\implies\,sec^2(\theta)-1=\dfrac{(41)^2}{(9)^2}-1}$

$\tt{\implies\,tan^2(\theta)=\dfrac{(41)^2-(9^2)}{(9)^2}}$

$\tt{\implies\,tan^2(\theta)=\dfrac{1681-81}{(9)^2}}$

$\tt{\implies\,tan^2(\theta)=\dfrac{1600}{(9)^2}}$

$\tt{\implies\,tan^2(\theta)=\dfrac{(40)^2}{(9)^2}}$

$\tt{\implies\,tan(\theta)=\dfrac{40}{9}}$