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Question
If –1 ≤ x ≤ 1, the prove that sin–1 x + cos–1 x = `π/2`
Solution
Let sin–1 x = θ, where x ∈ [–1, 1] and `θ ∈ [-π/2, π/2]`
∴ `- θ ∈ [-π/2, π/2]`
∴ `π/2 - θ ∈ [0, π]`, the principal domain of the cosine function.
∴ `cos(π/2 - θ)` = sin θ
`cos(π/2 - θ)` = x
∴ cos–1 x = `π/2 - θ`
∴ `θ + cos^-1x = π/2`
∴ sin–1 x + cos–1 x = `π/2`
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