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We provide a new proof of the trigonometric inequality obtained by K. S. K. Iyengar, B. S. Madhava Rao and T. S. Nanjundiah in 1945, and offer also the hyperbolic version of this result. Certain related results are pointed out, too.

On the Iyengar–Madhava Rao–Nanjundiah inequality and its hyperbolic version