Question

Evaluate 3cos80°cosec10° + 2sin59°cosec31°​

Answer 1

Answer:

5

Step-by-step explanation:

To Find :-

Value of :-

3 cos 80° cosec 10° +2 sin 59° sec 31°

Solution :-

3cos80°csc10° + 2sin59°sec31°

= 3cos80°csc(90° - 80°) + 2sin59°sec(90° - 59°)

[∴ 10 = 90 - 80 , 31 = 90 - 59]

= 3cos80°sec80° + 2sin59°csc59°

[∴ In first quadrant all ratios are positive ]

$=3cos80^{\circ}\times\dfrac{1}{cos80^{\circ}}+2sin59^{\circ}times\dfrac{1}{sin59^{\circ}}$

= 3 + 2

= 5

∴ 3 cos 80° cosec 10° +2 sin 59° sec 31° = 5.

Know More :-  

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\sf Trigonometry\: Table \\ \begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\boxed{\begin{array}{ |c |c|c|c|c|c|} \bf\angle A & \bf{0}^{ \circ} & \bf{30}^{ \circ} & \bf{45}^{ \circ} & \bf{60}^{ \circ} & \bf{90}^{ \circ} \\ \\ \rm sin A & 0 & \dfrac{1}{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{ \sqrt{3}}{2} &1 \\ \\ \rm cos \: A & 1 & \dfrac{ \sqrt{3} }{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{1}{2} &0 \\ \\ \rm tan A & 0 & \dfrac{1}{ \sqrt{3} }&1 & \sqrt{3} & \rm \infty \\ \\ \rm cosec A & \rm \infty & 2& \sqrt{2} & \dfrac{2}{ \sqrt{3} } &1 \\ \\ \rm sec A & 1 & \dfrac{2}{ \sqrt{3} }& \sqrt{2} & 2 & \rm \infty \\ \\ \rm cot A & \rm \infty & \sqrt{3} & 1 & \dfrac{1}{ \sqrt{3} } & 0\end{array}}}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}$