Step-by-step explanation:
sin θ = 5/13
[since sin² θ + cos² θ = 1 ]
(5/13)² + cos² θ = 1
cos² θ + 25/169 = 1
cos² θ = 1 - 25/169
cos² θ =
[tex] \frac{169 - 25}{169} [/tex]
cos² θ = 144/169
cos θ =
[tex] \sqrt{ \frac{144}{169} } [/tex]
cos θ = 12 /13
sec θ + tan θ =
1/ cos θ + sin θ / cos θ =
[tex] \frac{1}{ \frac{12}{13} } + \frac{5}{ \frac{13}{ \frac{12}{13} } } [/tex]
13/12 + 5/12 = 18/12
sec θ + tan θ = 6/4
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Verified answer
sin θ = 5/13sin^2 θ = 25/169
1 - sin^2 θ = 1 - 25/169
cos^2 θ = (169-25)/169
Since sin^2 θ + cos^2 θ = 1
Therefore cos θ = sqrt(144/169)
cos θ = 12/13
sec θ = 1/cos θ = 1/12/13 = 13/12
tan θ = sin θ / cos θ = 5/13 / 12/13 = 5/12
sec θ + tan θ = 13/12 + 5/12 = (13+5)/12 = 18/12
= 3/2
Answer:
3/2
PLEASE MARK BRAINLIEST
Step-by-step explanation:
sin θ = 5/13
[since sin² θ + cos² θ = 1 ]
(5/13)² + cos² θ = 1
cos² θ + 25/169 = 1
cos² θ = 1 - 25/169
cos² θ =
[tex] \frac{169 - 25}{169} [/tex]
cos² θ = 144/169
cos θ =
[tex] \sqrt{ \frac{144}{169} } [/tex]
cos θ = 12 /13
sec θ + tan θ =
1/ cos θ + sin θ / cos θ =
[tex] \frac{1}{ \frac{12}{13} } + \frac{5}{ \frac{13}{ \frac{12}{13} } } [/tex]
13/12 + 5/12 = 18/12
sec θ + tan θ = 6/4