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Question

sin15° cos75°+cos15° sin75°tan5° tan30° tan 35° tan 55° tan85°

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Solution

sin150cos750+cos150sin750tan50tan300tan350tan550tan850 =sin150cos(900150)+cos150sin(900150)tan300{tan50tan350tan550tan850} =sin150sin150+cos150cos15013{tan(90050)tan850.tan350tan(900350)} =sin2150+cos215013(cot850tan850)(tan350.cot350) =3(1tan850tan850)(1cot350.cot350) =31×1 =3

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