sin2x+cos2x 怎么得出等于 根号2sin(2x+派/4)

Question

如题所述

Answer 1

sin2x+cos2x
=asin2x+bcos2x
=√1+1（√2/2sin2x+√2/2cos2x）
=√2（cos派/4in2x+sin派/4cos2x)
=√2sin(2x+派/4)

Answer 2

sin2x+cos2x
=[(1/√2)sin2x+(1/√2)cos2x]*√2
=√2*[(√2/2)sin2x+(√2/2)cos2x]
=√2*[cosπ/4sin2x+sinπ/4cos2x]
=√2sin(2x+π/4)

Answer 3

(sin2x+cos2x)^2
=(sin2x)^2+(cos2x)^2+2*sin2xcos2x
=1+2sin2xcos2x
=2sin(pi/4)cos(pi/4)+2sin2xcos2x
=2sin(2x+pi/4)

Answer 4

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