Question

If αsin A = 5 and 7cosecA = 6 sec A, then the value of α is
(a) 46/45
(b) 46/7
(c)49/46
(d) None of these​

Answer 1

→ ɑ * sin A = 5

→ sin A = 5 / ɑ = P/H

So,

→ B = √(H² - P²) { By pythagoras theorem }

→ B = √(ɑ² - 25)

then,

→ tan A = P/B

→ tan A = 5/√(ɑ² - 25) ----------- Eqn.(1)

now,

→ 7•cosec A = 6•sec A

→ 7/6 = sec A / cosec A

→ 7/6 = (1/cos A)/(1/sin A)

→ 7/6 = (sin A/cos A)

→ 7/6 = tan A -------------- Eqn.(2)

from Eqn.(1) and Eqn.(2) we get,

→ 5/√(ɑ² - 25) = 7/6

→ 7•√(ɑ² - 25) = 5 • 6

→ √(ɑ² - 25) = 30/7

squaring both sides ,

→ (ɑ² - 25) = 900/49

→ ɑ² = (900/49) + 25

→ ɑ² = (900 + 1225)/49

→ ɑ² = (2125/49)

→ ɑ² = (46.09/7)²

→ ɑ = (46.09/7)

→ ɑ ≈ (46/7) (b) (Ans.)

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