In a right angled triangle, if tan θ θ = 34 3 4 . What is cosθ θ - sinθ θ ?

Assessment: JAMB UTME - Mathematics - 2011 Subject: General Mathematics

Question 1 Report

In a right angled triangle, if tan $θ$ = $\frac{3}{4}$ . What is cos $θ$ - sin $θ$ ?

$\frac{2}{3}$

\frac{3}{5}

\frac{1}{5}

\frac{4}{5}

Answer Details

tan $θ$ = $\frac{3}{4}$
from Pythagoras tippet, the hypotenus is T
i.e. 3, 4, 5.
then sin $θ$ = $\frac{3}{5}$ and cos $θ$ = $\frac{4}{3}$
cos $θ$ - sin $θ$
$\frac{4}{5}$ - $\frac{3}{5}$ = $\frac{1}{5}$

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