Question -
Answer -
Given,
sec θ = 13/5
We know that,
sec θ = 1/ cos θ
⇒ cos θ = 1/ sec θ = 1/ (13/5)
∴ cos θ = 5/13 ……. (1)
By definition,
cos θ = adjacent side/ hypotenuse ….. (2)
Comparing (1) and (2), we have
Adjacent side = 5 and hypotenuse = 13
By Pythagoras theorem,
Opposite side = √((hypotenuse) 2 – (adjacent side)2)
= √(132 – 52)
= √(169 – 25)
= √(144)
= 12
Thus, opposite side = 12
By definition,
tan θ = opposite side/ adjacent side
∴ tan θ = 12/ 5
From, let’s divide the numerator and denominator by cos θ.
We get,
(2 tan θ – 3) / (4 tan θ – 9)
⇒ (2(12/5) – 3) / (4(12/5) – 9) [using the value of tan θ]
⇒ (24 – 15) / (48 – 45) [After taking LCM and cancelling it]
⇒ 9/3 = 3
∴ = 3