If the inverse trigonometric functions take principal values, then cos - 1 3 10 cos tan - 1 4 3 + 2 5 sin tan - 1 4 3 is equal to

Question

If the inverse trigonometric functions take principal values, then cos - 1 3 10 cos tan - 1 4 3 + 2 5 sin tan - 1 4 3 is equal to, 0, π 4, π 3, π 6

MARKS App · Accepted Answer

Let tan - 1 4 3 = θ ⇒ tan θ = 4 3 ∴ cos θ = 3 5 & sin θ = 4 5 So, cos - 1 3 10 cos tan - 1 4 3 + 2 5 sin tan - 1 4 3 = cos - 1 3 10 cos θ + 2 5 sin θ = cos - 1 3 10 × 3 5 + 2 5 × 4 5 = cos - 1 9 50 + 8 25 = cos - 1 1 2 = π 3

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