Question

If sin(x) = 3/5, tan(y) = 1/2 and
$\frac{\pi}{2} < x < \pi < y < \frac{3\pi}{2}$
, find the value of
$8 \tan(x) - \sqrt{5} \sec(y)$


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Answer 1

Step-by-step explanation:

sinx = 3/5 => x = 37°

tan(y) = 1/2

√sec^2y - 1 = 1/2. { sec^2y = 1 + tan^2y}

sec^2y - 1 = 1/4

sec^2y = 3/4

sec y = (√3)/2

8 tanx -√5 sec y = 8tan37° - √5× (√3)/2

= 8×3/4 - √15/2

= 24 - √15/2

= (48 - √15)/2