Question

Find the value of :
3 cos 80° cosec 10° +2 sin 59° sec 31°.​

Answer 1

Answer:

5

Step-by-step explanation:

3cos80°cosec10°+2sin59°sec31°

=3sin10°cosec10°+2cos31°sec31°

=3(sin10°/sin10°)+2(cos31°/cos31°)

=3(1)+2(1)

=3+2

=5

Answer 2

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° - 10°) + 2sin59°sec(90° - 59°)

[∴ 10 = 90 - 80 , 31 = 90 - 59]

= 3cos80°sec10° + 2sin59°csc59°

[∴ In first quadrant all ratios are positive ]

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

$=3\times1 +2\times 1$

= 3 + 2

= 5

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