SOLUTION: How to establish the identities:
(sin(a-b))/(sin(a)cos(b))=1-cot(a)tan(b)
and
2sin(2theta)(1-2sin^2theta)=sin(4theta)
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-> SOLUTION: How to establish the identities:
(sin(a-b))/(sin(a)cos(b))=1-cot(a)tan(b)
and
2sin(2theta)(1-2sin^2theta)=sin(4theta)
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Question 608443: How to establish the identities:
(sin(a-b))/(sin(a)cos(b))=1-cot(a)tan(b)
and
2sin(2theta)(1-2sin^2theta)=sin(4theta) Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website! How to establish the identities:
(sin(a-b))/(sin(a)cos(b))=1-cot(a)tan(b)
Use addition formula for sin: sin(a-b)=sina*cosb-cosa*sinb
Start with left side:
(sin(a-b))/(sina*cosb)
=(sina*cosb-cosa*sinb)/(sina*cosb)
=1-(cosa*sinb)/(sina*cosb)
=1-cota*tanb
verified: left side=right side
..
and
2sin(2theta)(1-2sin^2theta)=sin(4theta)
use x for theta
Start with right side:
sin4x=2sin2xcos2x
=2sin2x(cos^2x-sin^2x)
=2sin2x(1-sin2^x-sin^2x)
=2sin2x(1-2sin^2x)
verified: right side=left side
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