If $cosec θ =\frac{\sqrt{5}}{2}$, then what will be the value of $(sec θ + tan θ- cotθ sinθ)$ ?
Answer & explanation
Correct answer: option 1
$cosec θ =\frac{\sqrt{5}}{2}$,
cosecθ = \(\frac{H}{P}\)
By using pythagoras theorem,
P² + B² = H²
2² + B² = √5²
B = 1
Now,
sec θ+ tanθ - cotθ. sinθ
= \(\frac{√5}{1}\) + \(\frac{2}{ 1 }\) - \(\frac{1}{2}\) . \(\frac{2}{√5}\)
= \(\frac{2 +√5 }{1}\) - \(\frac{1}{√5}\)
= \(\frac{2 +√5 }{1}\) - \(\frac{1}{√5}\)
= \(\frac{2√5 +5 - 1 }{√5}\)
= 2 + \(\frac{4√5 }{5}\)