Question

If $sin\theta =\frac{4}{5}$ , Find the value of $\frac{4tan\theta -5cos\theta }{sec\theta +4cot\theta }$

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

$sin\theta =\frac{4}{5},1-si{n}^2\theta =co{s}^2\theta cos\theta =\frac{3}{5}$
$tan\theta =\frac{sin\theta }{cos\theta }$
$\Rightarrow tan\theta =\frac{4}{3}$
$sec\theta =\frac{1}{cos\theta }$
$\Rightarrow sec\theta =\frac{5}{3}$
$cot\theta =\frac{1}{tan\theta }$
$\Rightarrow cot\theta =\frac{3}{4}$​
For the given values of trigonometric ratios, the value of the expression is $\frac{1}{2}$