Question

If tan theta =5/12 , Find the value of sec
theta

Answer 1

Answer:

Tan α = 5/12

From trig ratio [triangle]

Tan alpha = Opposite side/Adjacent side = 5/12

Hence, Hypotenuse = √(52 + 122) = √(25+144) = √169 = 13

Sec α = 1/cos α = hypotenuse/adjacent side = 13/12

Sec α = 13/12

Answer 2

The value of sec theta is 13/12.

Given:

Tan theta =5/12

To find:

Sec theta

Solution:

We can simply substitute the given value of tan theta in the following identity-

We know that the difference between the squares of sec theta and tan theta is equal to 1.

$sec^{2} theta$ - $tan^{2} theta$ =1

Using the value of tan theta, we get

$sec^{2} theta$ - $(5/12)^{2}$=1

$sec^{2} theta$ =1+25/144

$sec^{2} theta$ = (144+25)/144

$sec^{2} theta$ =169/144

sec theta=√(169/144)

sec theta=13/12

Therefore, the value of sec theta is 13/12.