Express cos4⁢x+4⁢cos2⁢x+3⁢ in terms of cosx.
There are three forms for the double-angle formula for the cosine function:
= 2 cos2x−1
= 1−2 sin2x
Apply the second form of the expansion formula to cos2⋅2 x to obtain
= 2 cos22 x−1
= 22 cos2x−12−1
= 24 cos4x−4 cos2x+1−1
= 8 cos4x−8 cos2x+1
Combine both results to obtain
=8 cos4x−8 cos2x+1+42 cos2x−1+3
=8 cos4x−8 cos2x+8 cos2x+1−4+3
Control-drag the given expression.
Context Panel: Expand≻Expand
cos4⁢x+4⁢cos2⁢x+3= expand 8⁢cos⁡x4
Control-drag the first term.
cos4 x= expand 8⁢cos⁡x4−8⁢cos⁡x2+1
Control-drag the second term.
4⁢cos2⁢x= expand 8⁢cos⁡x2−4
Add the two expanded expressions and add 3. The sum is 8 cos4x.
Assign the name q__1 to the given expression.
Apply the expand command to the whole expression.
Apply the expand command to the first term.
Apply the expand command to the second term.
Sum the sub-expressions
Add the sub-expressions.
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