Question

The value of $\frac{2sec 52\textdegree}{3 cosec 38\textdegree} -\frac{sin37\textdegree}{2 cos53\textdegree}$ is:
(A) 1
(B)$\frac{1}{6}$
(C) $-\frac{1}{6}$
(D) 1

Answer 1

Answer: option B
$\frac{1}{6}$

Solution:

$\frac{2 \: sec \: 52°}{3 \: cosec \: 38° } - \frac{sin \: 37°}{2 \: cos \: 53°}$
we know that complementary angle formula

$sin \: (90° - \theta) = cos \: \theta \\ sec(90° - \theta) = cosec \: \theta$
So,apply these formulas

$= \frac{2 \: sec \: 52°}{3 \: cosec \: 38° } - \frac{sin(90° - 53°)}{2 \: cos \: 53°}\\ \\ =\frac{2 \: sec \: (90° - 38°)}{3 \: cosec \: 38°} - \frac{cos \: 53°}{2 \: cos \: 53°} \\ \\ =\frac{2 \: cosec \: 38°}{3 \: cosec \: 38° } - \frac{1}{2} \\ \\ =\frac{2}{3} - \frac{1}{2} \\ \\ = \frac{4 - 3}{6} \\ \\ = \frac{1}{6}$
Hope it helps you.