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tignometry query

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spiderman:
Prove the following identity

(1-2sin^2@)/(cos@+sin@)==cos@-sin@


Pls help someone

Ghost Of Highbury:

--- Quote from: spiderman on September 15, 2009, 11:50:36 am ---Prove the following identity

(1-2sin^2@)/(cos@+sin@)==cos@=sin@


Pls help someone

--- End quote ---
wats the "=="

and how can cos @ = sin @
is the q correct?

spiderman:
== means that we have to solve the left hand side to get an answer matching the rhs

astarmathsandphysics:
think the rhs should be cos@-sin@
multuply both sides by cos@+sin@ to get
1-2sin2@=(cos@+sin@)(cos@-sin@)=cos2@-sin2@=cos2@

1-2sin2@=cos2@ is an identity

Ghost Of Highbury:

--- Quote from: eddie_adi619 on September 15, 2009, 12:15:42 pm ---wats the "=="

and how can cos @ = sin @
is the q correct?

--- End quote ---

ok..i assume this is the question

(1-2sin^2@)/(cos@+sin@)= cos@ - sin@

the answer-----------

1 - 2sin2@ = sin2@ + cos2@ - 2sin2@ = cos2@ - sin2@

cos2@ - sin2@ = (cos @ + sin @) (cos @ - sin @)

wen u divide it by (cos@+sin@)

it is = (cos @ + sin @) (cos @ - sin @) / (cos@+sin@) = (cos @ - sin @)

therefore LHS = RHS

is this the question?

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