In a right angled triangle, if tan \(\theta\) = \(\frac{3}{4}\). What is cos\(\theta\) - sin\(\theta\)?
A
\(\frac{2}{3}\)
B
\(\frac{3}{5}\)
C
\(\frac{1}{5}\)
D
\(\frac{4}{5}\)
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
tan\(\theta\) = \(\frac{3}{4}\)
from Pythagoras tippet, the hypotenus is T
i.e. 3, 4, 5.
then sin \(\theta\) = \(\frac{3}{5}\) and cos\(\theta\) = \(\frac{4}{5}\)
cos\(\theta\) - sin\(\theta\)
\(\frac{4}{5}\) - \(\frac{3}{5}\) = \(\frac{1}{5}\)
Source: Myschool Past Questions Archive (Record #29486)