If α = sin - 1 ⁡ 3 2 + sin - 1 ⁡ 1 3 and β = cos - 1 ⁡ 3 2 + cos - 1 ⁡ 1 3 , then

Question

If α = sin - 1 ⁡ 3 2 + sin - 1 ⁡ 1 3 and β = cos - 1 ⁡ 3 2 + cos - 1 ⁡ 1 3 , then, α > β, α = β, α β, α + β = 2 π

MARKS App · Accepted Answer

α + β = sin - 1 ⁡ 3 2 + cos - 1 ⁡ 3 2 + sin - 1 ⁡ 1 3 + cos - 1 ⁡ 1 3 = π 2 + π 2 = π Also, α = π 3 + sin - 1 ⁡ 1 3 π 3 + sin - 1 ⁡ 1 2 As sin ⁡ θ is increasing in 0 , π 2 ∴ α π 3 + π 6 = π 2 ⇒ β > π 2 > α ⇒ α β

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