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Message: <blockquote data-quote="imhotep" data-source="post: 30031439" data-attributes="member: 562115">Can anyone simplify Tan^-1 (Tan 50 * Tan 10)/ Tan20 ?....More on this... another method using Feynman's Morrie's Law. Feynman was told about this by a childhood friend Morrie. It's the identitycos(20). cos(40). cos(80) = 1/8A similar identity for the sines exist and it's sin(20).sin(40).sin(80) =  √3/8Dividing these two together gives us tan(20).tan(40).tan(80) =  √3 = tan(60)Note that tan(10) is the inverse of tan(80), and tan(40) is the inverse of tan(50).  We immediately have the result.FYI... Morrie's Law is a special case with n = 3 and α = 20° of the following generalised identity.<a href="https://imgbox.com/mKssaFNU" target="_blank"><img src="https://thumbs2.imgbox.com/83/ae/mKssaFNU_t.jpg" alt="" class="fr-fic fr-dii fr-draggable " style="" /></a></blockquote>

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