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प्रश्न
Prove the following:
`tan^-1["cosθ + sinθ"/"cosθ - sinθ"] = pi/(4) + θ, if θ ∈ (- pi/4, pi/4)`
उत्तर
L.H.S. = `tan^-1["cosθ + sinθ"/"cosθ - sinθ"]`
= `tan^-1 [((cosθ)/(cosθ) + (sinθ)/(cosθ))/((cosθ)/(cosθ) - (sinθ)/(cosθ))]`
= `tan^-1((1 + tanθ)/(1 - tanθ))`
= `tan^-1[(tan pi/4 + tanθ)/(1 - tan pi/4 tan θ)]`
= `tan^-1[tan(pi/4 + θ)]`
= `pi/(4) + θ` ...[∵ tan–1(tan θ) = θ]
= R.H.S.
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