How many of following are matched correctly
Column AColumn B1. Sin 780∘a.√322. tan 1485∘b.−13. Cos 1350∘c.−14. Sec (−1920∘)d.−25. tan 2340∘e.06. cosec (−765∘)f.−27. Cot 600∘g.√38. Sin 3105∘h.−1√29. Sin (−3105∘)i.1√210. Cos 480∘j.−1√2Let's find the values of each trigonometric function.
(1).Sin 780∘
If we add 360 to an angle, it gives the same effective angle or by rotating the radius by 360, we reach the same position.
780∘ can be written as (2 × 360∘ + 60∘)
Sin (2 × 360∘ + 60∘) = sin 60∘ = √32 (correctly matched)
2.tan1485∘ = tan (4 × 360∘ + 45∘)
= tan 45∘ = 1 (Not correctly matched)
3.Cos 1350∘ = cos (3 × 360 + 270∘)
= cos 270∘ = cos (360 - 90∘)
= cos 90∘ = 0 (Not correctly matched)
4.Sec (-1920∘) = sec 1920∘ {sec (-θ) = sec θ}
Sec (5 × 360∘ + 120∘) = sec 120∘
= sec (180-60∘) = - sec 60∘ = -2 (correctly matched)
5.tan 2340∘ = tan (6 × 360∘ + 180∘) = tan 180∘ = 0 (correctly matched)
6. cosec(-765∘) = - cosec 765∘ = -cosec(2 × 360∘ + 45∘)
= -cosec 45∘ = −√2(Not correctly matched)
7. Cot 600∘ = Cot(360 + 240) = cot240∘
= cot(180∘ + 60∘) = cot 60∘ = 1√3 (Not correctly matched)
8. Sin 3105∘ = sin (8 × 360∘ + 225∘) = sin(225∘)
= sin (180∘ + 45∘) = -sin 45∘ = −1√2 (Correctly matched)
9. Sin(-3105∘) = -sin 3105∘ = −(−1√2) = 1√2(Correctly matched)
10. Cos 480∘ = cos(360∘ + 120∘) = cos 120∘
= cos(180∘ - 60∘) = -cos60∘ = −12 (Not Correctly matched)
So, 5 values are correctly matched.