Page 99 - Math Grade 11 (Basic)

PROEUS DARA

3.

3.1 ui rnt.:~fi~ rnn ruu Wfm ~ rnun
I U
m'!Wu'iHl a rnu n sl:l a rn 1::1 n 21l:l ~ um'l:3
u 61 u
cos(a-~) = cosacos~+sinasin~ (1), cos(a+~) = cosacos~-sinasin~ (2)

sin( a+~) = sin a cos~+ sin~cosa ( 3) , sin(a-~) = sinacos~-sin~cosa (4)

fi. UfiH5'HS (I ) sb (2) t f:1 Ql S cos (a + ~) + cos (a - ~) = 2 cos a cos ~
u u ...
1:lnams (1) sh (2) tf:1QlS cos(a+~)-cos(a-~) = -2sinasin~ '1
u ...
~. 'i5fiH5'HS (3) sb (4) tf:1QlS sin(a+~)+sin(a-~) = 2sinacos~
u u ...
1:lnm-es (3) sh (4) tf:1QlS sin (a + ~) - sin (a ~) = 2sin~cosa '1
u ...

cosacos~ = ~[cos(a+~)+cos(a-~)], sinasin~ = ~[cos(a-~)-cos(a+~)]

sin a cos~ = ~[sin( a+~)+ sin( a-~)] , sin~cosa = ~[sin( a+~)- sin( a-~)]

1 1
cos75°cos45° = [cos(75°+45°)+cos(75°-45°)] = (cos120°+cos30°)
2 2
= ! (- ! + J3) = J3 - 1 '1
2 2 2 4
2n) J
=
+
cos
sm sm = (5n n) -cos (5n n) J 1 [( n - cos
. Sn . n 1 [ cos
12 4 2 12 4 12 4 2 6 3
1
= H f-(- ~) J = J34+ '1
3.2 Ulntilfit'SntUniWfthtSntfirul
U I
mha+f.\=p ,a ~=q tf:19lmQlSa=p+q Sl:i~=p-q'1dShla Sl:i~
p ....., 2 2 1J

cos p + cos q = 2 cos p + q cos p - q cos p - cos q = -2 sin p + q sin P - q
2 2 , 2 2
sinp + sinq = 2sinp + q cosp- q sinp- sinq = 2sinp- q cosp + q
2 2 ' 2 2

sinp sinq sinpcosq + sinqcosp _ sin(p + q)
tanp+tanq = --+- = '1
cos p cosq cos pcosq cos pcosq

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