Question

cos80/sin10 + cos59×cosec31

Answer 1

$\star\:\:\:\bf\large\underline\blue{Question:-}$

• Evaluate $\frac{ \cos80\degree}{ \sin10 \degree } + \cos59 \degree \times \cosec31 \degree$

$\star\:\:\:\bf\large\underline\blue{Solution:-}$

• Before we start, we have to know the formula to solve the problem.
• Complementary angle formulae are needed while solving this kinds of problems.
• Two angles are said to be complementary angle if the sum of the angles is 90°.

$\star\:\:\:\bf\large\underline\blue{Formula\:To\:Be\:Used:-}$

• $\sin(90 \degree - \theta) = \cos \theta$
• $\cos(90\degree-\theta) =\sin\theta$

Now, we will solve the problem. Given--

$\frac{ \cos80\degree}{ \sin10 \degree } + \cos59 \degree \times \cosec31 \degree$

$= \frac{ \cos80\degree}{ \sin10 \degree } + \cos59 \degree \times \frac{1}{ \sin31 \degree}$

$= \frac{ \cos80\degree}{ \sin(90 \degree - 80 \degree)} + \frac{ \cos59 \degree }{ \sin(90 \degree -59\degree)}$

$= \frac{ \cancel{ \cos80 \degree}}{ \cancel{\cos 80\degree}} + \frac{ \cancel{ \cos59 \degree}}{ \cancel{\cos59 \degree}}$

$= 1 + 1$

$= 2$

$\star\:\:\:\bf\large\underline\blue{Answer:-}$

• Answer for the problem is 2.