The value of 2 sin - 1 ⁡ 4 5 + 2 sin - 1 ⁡ 5 13 + 2 sin - 1 ⁡ 16 65 is equal to

Question

The value of 2 sin - 1 ⁡ 4 5 + 2 sin - 1 ⁡ 5 13 + 2 sin - 1 ⁡ 16 65 is equal to, 3 π 2, π 2, π, 2 π

MARKS App · Accepted Answer

2 sin - 1 ⁡ 4 5 + sin - 1 ⁡ 5 13 + sin - 1 ⁡ 16 65 = 2 sin - 1 ⁡ 4 5 1 - 5 13 2 + 5 13 1 - 4 5 2 + 2 sin - 1 ⁡ 16 65 = 2 sin - 1 ⁡ 48 65 + 15 65 + 2 sin - 1 ⁡ 16 65 = 2 sin - 1 ⁡ 63 65 + sin - 1 ⁡ 16 65 = 2 cos - 1 ⁡ 16 65 + sin - 1 ⁡ 16 65 ∵ sin - 1 ⁡ x = cos - 1 ⁡ 1 - x 2 = π

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