Use the double angle formulas to verify the identity.
Start with the left hand side and try to get to the right hand side:
sin(4x)=sin[2(2x)] Use sin2A=2sinAcosA:
=2sin(2x)cos(2x) Again use sin2A=2sinAcosA:
=2[2sin(x)cos(x)cos(2x)]
=4sin(x)cos(x)cos(2x)
Here we have a choice for cos(2x) -- choose 2cos^2x-1
=4sin(x)cos(x)[2cos^2(x)-1] Multiply to get:
=8cos^3(x)sin(x)-4sin(x)cos(x) as required.
Use the double angle formulas to verify the identity. Use the double angle formulas to verify...
DOUBLE ANGLE IDENTITIES: In excercises 24-42, Verify each identity. #’s 25, 29, 33, 37, 41 please and thank you! In Exerci 23. cs 25>(sinx-cosx)(cosx + sinx) =-cos(2x) ises 23-42, verify each identity. o(24)= cscA secA 1 + cos(2x ) 27. cos2x= cost-sin4x = cos(2x) 31. 8sin2xcos2x= 1-cos(4x 33)- sec2x =-2 sin?rcsc"(2x) 35. sin(3x) = sinx(4cos2x-1) 39, sin(4x) = sin(2x)(2-4sin%) G) sin(4x) = 2sinx cosx-4sin3x cos tan(4x) = 4(sinx)(cosx)[cos(2x)] 1 2sin (2x)
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Use a double-angle identity to find the exact value of the expression. 2 cos 267.5° - 1 - 2
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using double angle identity solve 10sin2x+cosx =0
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