Question

if tan alphe=5/12, find the value of sec alphe

Answer 1

Answer:

13/12

Step-by-step explanation:

You got Set 2 in board exam right??

So:

In a triangle ABC, Tan alpha = AB/BC = 5/12

Therefore AB = 5x and BC = 12x (Where x is some positive integer)

By pythagoras theorem, we get AC = 13x

Sec alpha = AC/BC = 13x/12x = 13/12

Therefore sec alpha = 13/12

Answer 2

       

$\tan\alpha=\frac{5}{12} \\ \\ \\ \tan^2\alpha=(\frac{5}{12})^2 \\ \\ \Rightarrow\ \tan^2\alpha=\frac{25}{144}$

$\sec^2\alpha-\tan^2\alpha=1 \\ \\ \Rightarrow\ \sec^2\alpha-\frac{25}{144}=1 \\ \\ \Rightarrow\ \sec^2\alpha=1+\frac{25}{144} \\ \\ \Rightarrow\ \sec^2\alpha=\frac{169}{144} \\ \\ \Rightarrow\ \sec\alpha=\sqrt{\frac{169}{144}} \\ \\ \Rightarrow\ \sec\alpha=\pm \frac{13}{12}$

$[ \sf{The values are applied for a right triangle of sides in the ratio 5:12:13.} \ ]$

$\sf{Plz mark it as the brainliest. \\ \\ \\ Thank you. :-))}$