Given:
sec θ = 13/12
To find:
(1-tanθ) / (1+tanθ) = ?
Solution:
We always need to approach these types of trigonometric questions by visualizing a right-angled triangle and its perpendicular, base, and hypotenuse.
We know,
cos θ = [tex]\frac{Base}{Hypotenuse}[/tex]
and,
sec θ = 1 / cos θ
therefore,
sec θ = [tex]\frac{Hypotenuse}{Base}[/tex]
Again, sec θ = 13/12
therefore, we have,
Hypotenuse (h) = 13
Base (b) = 12
Now,
By applying the Pythagoras theorem we can get perpendicular (p).
i.e,
p² + b² = h²
or, p² = h² - b²
or, p² = 13² - 12²
= 169 - 144
= 25
or, p = √25
or, p = 5
So, we get the perpendicular (p) as 5.
tan θ = [tex]\frac{Perpendicular}{Base}[/tex]
that means, from what we have as p, h and b.
tan θ = 5/13
(1-tanθ) / (1+tanθ) = [tex]\frac{1-\frac{5}{12} }{1+\frac{5}{12} }[/tex]
= [tex]\frac{\frac{7}{12} }{\frac{17}{12} }[/tex]
=[tex]\frac{7}{17}[/tex]
Thus the required answer of (1-tanθ) / (1+tanθ) is 7/17
Hence, (1-tanθ) / (1+tanθ) = 7/17
Answer:
Step-by-step explanation:
consider a right-angled triangle with an acute angle thita
sec thita = hypotenuse/adjacent side length
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Verified answer
Given:
sec θ = 13/12
To find:
(1-tanθ) / (1+tanθ) = ?
Solution:
We always need to approach these types of trigonometric questions by visualizing a right-angled triangle and its perpendicular, base, and hypotenuse.
We know,
cos θ = [tex]\frac{Base}{Hypotenuse}[/tex]
and,
sec θ = 1 / cos θ
therefore,
sec θ = [tex]\frac{Hypotenuse}{Base}[/tex]
Again, sec θ = 13/12
therefore, we have,
Hypotenuse (h) = 13
Base (b) = 12
Now,
By applying the Pythagoras theorem we can get perpendicular (p).
i.e,
p² + b² = h²
or, p² = h² - b²
or, p² = 13² - 12²
= 169 - 144
= 25
or, p = √25
or, p = 5
So, we get the perpendicular (p) as 5.
Now,
We know,
tan θ = [tex]\frac{Perpendicular}{Base}[/tex]
that means, from what we have as p, h and b.
tan θ = 5/13
i.e,
(1-tanθ) / (1+tanθ) = [tex]\frac{1-\frac{5}{12} }{1+\frac{5}{12} }[/tex]
= [tex]\frac{\frac{7}{12} }{\frac{17}{12} }[/tex]
=[tex]\frac{7}{17}[/tex]
Thus the required answer of (1-tanθ) / (1+tanθ) is 7/17
Hence, (1-tanθ) / (1+tanθ) = 7/17
Answer:
Step-by-step explanation:
consider a right-angled triangle with an acute angle thita
sec thita = hypotenuse/adjacent side length