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Question
Given : 17 cos θ = 15;
Find the value of: tan θ + 2 secθ .
Solution
Consider the diagram below :
17 cos θ = 15
cos θ = `(15)/(17)`
i.e `"base"/"hypotenuse" = (15)/(17) ⇒ "AB"/"AC" = (15)/(17)`
Therefore if length of AB = 15x, length of AC = 17x
Since
AB2 + BC2 = AC2 ...[ Using Pythagoras Theorem ]
(17x)2 – (15x)2 = BC2
BC2 = 64x2
∴ BC = 8x ...( perpendicular)
Now
sec θ = `"AC"/"AB" = (17)/(15)`
tan θ = `"BC"/"AB" = (8)/(15)`
Therefore
tan θ +2 sec θ
= `(8)/(15) + 2. (17)/(15)`
= `(42)/(15)`
= `(14)/(5)`
= `2(4)/(5)`
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