Math masters, Yura s formula, double angle formula, etc., are you rote memorizing? 30

Normally, it's not that hard to remember.

Sine double angle formula:

sin2 =2cos sin derivation: sin2a=sin(a+a)=sinacosa+cosasina=2sinacosa extended formula: sin2a=2sinacosa=2tanacosa 2=2tana [1+tana 2] 1+sin2a=(sina+cosa) 2

Cosine double angle formula:

The formula for cosine doubling angle has three sets of representations, and the three sets of forms are equivalent: Derivation: cos2a=cos(a+a)=cosacosa-sinasina=(cosa) 2-(sina) 2=2(cosa) 2-1 =1-2(sina) 2

Tangent double angle formula:

tan2 =2tan [1-(tan) 2] derived: tan2a=tan(a+a)=(tana+tana) (1-tanatana)=2tana [1-(tana) 2].

Exponential formula: cosa 2=[1+cos2a] 2 sina 2=[1-cos2a] 2 variant modulus vertical void: sin2 =sin2 + 4-cos2 +4 =2sin2a+4 -1=1-2cos2 +4 ; cos2α=2sinα+4πcosα+4π

First, list the relevant equations for doubling angles, sin2a = 2sinacosa, sin(180-a) = sina, cos2a = cos 2a-sin 2a. (1) 2sin20cos20=sin40,1 2sim80=sin40cos40,1 4sin160=1 2sin80cos80, that is, cos20cos40cos80=(1 4sin160) 2sin(180-160)=sin160 8sin160=1 8. (2) cos(a-b)=-4 5 and (a-b) belongs to the second quadrant, so sin(a-b)=3 5, cos(a b)=4 5 and (a b) belongs to the fourth quadrant, so sin(a b)=-3 5, cos2a=cos[(a-b) (a b)]=cos(a-b)cos(a b)-sin(a-b)sin(a b)=-4 5x4 5-3 5x(-3 5)=-7 25, if you are not mistaken.

Just follow the prompts, using the doubling formula, sin2x=2sinx cosx

Multiply and divide by 2sin20°, then the original formula = sin160° 4 2sin20° = 1 8

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