Double Angle Identities
Key Questions
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Answer:
As below.
Explanation:
Following table gives the double angle identities which can be used while solving the equations.
You can also have
#sin 2theta, cos 2theta# expressed in terms of#tan theta # as under.#sin 2theta = (2tan theta) / (1 + tan^2 theta)# #cos 2theta = (1 - tan^2 theta) / (1 + tan^2 theta)# 
sankarankalyanam
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1
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Mar 9 2018
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You would need an expression to work with.
For example:
Given#sinalpha=3/5# and#cosalpha=-4/5# , you could find#sin2 alpha# by using the double angle identity
#sin2 alpha=2sin alpha cos alpha# .#sin2 alpha=2(3/5)(-4/5)=-24/25# .You could find
#cos2 alpha# by using any of:
#cos2 alpha=cos^2 alpha -sin^2 alpha#
#cos2 alpha=1 -2sin^2 alpha#
#cos2 alpha=2cos^2 alpha -1# In any case, you get
#cos alpha=7/25# .
Jim H
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1
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Mar 6 2015
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#sin2theta=2sin theta cos theta# #cos2theta=cos^2theta-sin^2theta=2cos^2theta-1=1-2sin^2theta# #tan2theta={2tan theta}/{1-tan^2theta}#
I hope that this was helpful.
Wataru
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1
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Nov 6 2014