Published by:
CGP EDU Academic Team
Published on: September 12, 2026
If tan θ = 
and θ lies in the first quadrant, the value of cos θ is :
A
B
– 
C
D
– 
Text Solution
Verified by ExpertsThe correct answer is:
C
Step 1: Given that \( \tan \theta = \frac{3}{4} \), we can identify the opposite side as 3 and the adjacent side as 4 in a right triangle.
Step 2: Using the Pythagorean theorem, calculate the hypotenuse:
\( h = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \).
Step 3: Now, we can find \( \cos \theta \) using the definition:\
\( \cos \theta = \frac{\text{Adjacent}}{\text{Hypotenuse}} = \frac{4}{5} \).
Step 4: Therefore, the value of \( \cos \theta \) is \( \frac{4}{5} \).
Hence, the correct answer is Option C.
Step 2: Using the Pythagorean theorem, calculate the hypotenuse:
\( h = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \).
Step 3: Now, we can find \( \cos \theta \) using the definition:\
\( \cos \theta = \frac{\text{Adjacent}}{\text{Hypotenuse}} = \frac{4}{5} \).
Step 4: Therefore, the value of \( \cos \theta \) is \( \frac{4}{5} \).
Hence, the correct answer is Option C.
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