evaluate tan^-1 [tan (5pi/6) + cos^-1 [cos (13pi/6)]

We havπetan-1tan5π6+cos-1cos13π6=tan-1tanπ-π6+cos-1cos2π+π6=tan-1-tanπ6+cos-1cosπ6                   As, tanπ-θ=-tanθ   and  cos2π+θ=cosθ =tan-1tan-π6+cos-1cosπ6=-π6+π6                As, tan-1tanθ=θ, for all  -π2<θ<π2   and  cos-1cosθ=θ, for all 0θπ=0Therefore,tan-1tan5π6+cos-1cos13π6=0

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