If tan A + sec A = 5, then what is the value of tan A?
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Correct answer: B
Explanation
The correct answer is option 2 i.e. .
tan A + sec A = 5
Let t = tan A
sec A = √(1 + t2)
t + √(1 + t2) = 5
⇒ √(1 + t2) = 5 – t
⇒ √(1 + t2) = (5 – t)2
⇒ 1 + t2 = 25 – 10t + t2
⇒ 1 = 25 – 10t
⇒ 10t = 24
⇒ t = 24/10 = 12/5
⇒ tan A = 12/5