tignometry query

[spiderman]

Prove the following identity

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


Pls help someone

[Ghost Of Highbury]

Prove the following identity

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


Pls help someone

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]

wats the "=="

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

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?

[spiderman]

Tahnks ssooo much

[spiderman]

Please can someone help me with the 4th question in the attached past paper

[astarmathsandphysics]

i)The equilibrium is at y=3. c=3, the displacement of the curve from equilibrium. The amplitude a =6 and the perid from the gaph is pi so b=2pi/pi=2

ii)y=0 so 6sin(2x)+3=0 so sin(2x+3)=-0.5 so
2x=sin^-1-0.5=-30

2x=180--30=210 x=105
2x=360+-30=330 so x=165
2x=540--30=570 so x=285
2x=720+-30=690 so x=345

[spiderman]

Thank you so much astar