Problem

(2sin⁡x+cos⁡x)2+(2cos⁡x−sin⁡x)2=5

Answer

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Hide Steps
Answer

=5(sin2⁡x+cos2⁡x)

Steps

Step 1 ：(2sin⁡x+cos⁡x)2+(2cos⁡x−sin⁡x)2=(2sin⁡x)2+2⋅2sin⁡x⋅cos⁡x+(cos⁡x)2+(2cos⁡x)2−2⋅2sin⁡x⋅cos⁡x+(sin⁡x)2

Step 2 ：=4(sin⁡x)2+4(cos⁡x)2+(sin⁡x)2+(cos⁡x)2

Step 3 ：=5(sin2⁡x+cos2⁡x)

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