Value of sec(t) is ±13/12 using the Pythagorean Trigonometric Identities and value of cos(t) is 12/13 using Reciprocal Trigonometric Identities.
There are three Pythagorean Trigonometric Identities listed below.
The value of trigonometry function is given as,
[tex]\tan(t)= \dfrac{5}{12}[/tex]
Here, the value of t lies between,
[tex]0 < t < \dfrac{\pi}{2}[/tex]
Use the Pythagorean Trigonometric Identities identity to start to solve the problem,
[tex]\sec^2{(t)}=\tan^2(t)+1[/tex]
Put the value of tangent, to find the value of secant,
[tex]\sec^2{(t)}=(\dfrac{5}{12})^2+1\\\sec^2{(t)}=\dfrac{25}{144}+1\\\sec^2{(t)}=\dfrac{25+144}{144}\\\sec^2{(t)}=\dfrac{169}{144}\\\sec^2{(t)}=\left(\dfrac{13}{12}\right)^2\\\sec(t)=\pm \dfrac{13}{12}[/tex]
Use the Reciprocal Trigonometric Identities identity can you now use to find cos(t),
[tex]\cos t=\dfrac{1}{\sec(t)}\\\cos t=\dfrac{12}{13}[/tex]
Hence, the value of sec(t) is ±13/12 using the Pythagorean Trigonometric Identities and value of cos(t) is 12/13 using Reciprocal Trigonometric Identities.
Learn more about the Pythagorean Trigonometric Identities here;
https://brainly.com/question/27029965
