Question

If 5tan alpha is equal to 4 then find sec alpha USING SUITABLE IDENTITY

Answer 1

Answer:

If 5tanα = 4, then the value of secα will be $\frac{\sqrt{41} }{5}$.

Step-by-step explanation:

Given that,

5tanα = 4

⇒ $tan\alpha = \frac{4}{5}$

Now, there is a trigonometric identity which is:

$tan^{2}\alpha + 1 = sec^{2} \alpha$

Putting the value of tanα in this equation, we get:

$tan^{2}\alpha + 1 = sec^{2} \alpha$

⇒ $(\frac{4}{5})^{2} + 1 = sec^{2} \alpha$

⇒ $1 + \frac{16}{25} = sec^{2} \alpha$

⇒ $\frac{25 + 16}{25} = sec^{2} \alpha$

⇒ $sec^{2} \alpha = \frac{41}{25}$

⇒ $sec\alpha = \sqrt{\frac{41}{25} }$

⇒ $sec\alpha = \frac{\sqrt{41} }{5}$

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