<prompt> Rahisishafractan 30circ tan 40circ tan 50circ tan 60circcos 20circ.  <response>: Kwa ujumla, kutoka kwa formula ya kuongeza pembe,anzaaligntan x tan y fracsin xcos x fracsin ycos y fracsin x cos y sin y cos xcos x cos y fracsin x ycos x cos y.mwishoalignHivyo,anzaalignfractan 30circ tan 40circ tan 50circ tan 60circcos 20circ fracfracsin 70 circcos 30circ cos 40circ fracsin 110circcos 50circ cos 60circcos 20 circ frac1cos 30circ cos 40circ frac1cos 50circ cos 60circ frac2sqrt3 cos 40circ frac2cos 50circ 2 cdot fraccos 50circ sqrt3 cos 40circsqrt3 cos 40circ cos 50circ 4 cdot fracfrac12 cos 50circ fracsqrt32 cos 40circsqrt3 cos 40mduara cos 50circ 4 cdot fraccos 60circ sin 40circ sin 60circ cos 40circsqrt3 cos 40circ cos 50 mduara.mwishoalignKutoka kwa fomula ya kuongeza pembe na bidhaa hadi jumla,anzaalign4 cdot fraccos 60circ sin 40circ sin 60circ cos 40circsqrt3 cos 40circ cos 50circ 4 cdot fracsin 60circ 40circsqrt3 cdot frac12 cos 90circ cos 10 circ frac8 sin 100circsqrt3 cos 10circ frac8 cos 10circsqrt3 cos 10circ frac8 sqrt33.mwishopanga 