If sec θ + tan θ = 5, and θ lies in the first quadrant, find the value of sin θ.
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Correct answer: B
Explanation
Given:
secθ + tanθ = 5, θ is in the first quadrant.
By the formula:
(secθ + tanθ)(secθ − tanθ) = 1
sinθ = tanθ / secθ
secθ − tanθ = 1/5
Now
secθ + tanθ = 5
secθ − tanθ = 1/5
2secθ = 5 + 1/5 = 26/5
secθ = 13/5
2tanθ = 5 − 1/5 = 24/5
tanθ = 12/5
sinθ = tanθ / secθ = (12/5) / (13/5) = 12/13