化简三角比的值cos2a +tan 2a .cos2a

题目

化简三角比的值cos2a +tan 2a .cos2a

答案

tan2a=sin2a/cos2a
所以cos2a+tan2a.cos2a=cos2a+(sin2a/cos2a)cos2a=cos2a+sin2a
=√2(sin2a*√2/2+cos2a*√2/2)
=√2(sin2acosπ/4+cos2asinπ/4)
=√2sin(2a+π/4)