[ŞEVVAL58]

s-1)a=arctan2-arctan1/2 ise tana=? (3/4)

s-2)arctan1/3+ arctan2/3= xise tan x=? (9/7)

s-3)tan(arctan1/5 +atctan3) =? (8)

s-4)arctan1/2+arctan1/3=? (pi/4)

s-5)cos(arccos12/13 + arcsin8/17) =? (140/221)

lütfen yardım edin nolur

[Serkan A.]

C-1) arctan2=a ve arctan1/2=b olsun. Ozaman tana=2 ve tanb=1/2 olur.

tan x=tan(a-b)=

tana-tanb

1+tana.tanb

=

2-(1/2)

1+2.(1/2)

=

3

4

C-2) tan x=

tan(arctan1/3)+ tan(arctan2/3)

1-tan(arctan1/3).tan(arctan2/3)

1/3+ 2/3

1-(1/3).(2/3)

=

9

7

C-3) tan(arctan1/5 +atctan3)=

(1/5)+3

1-(1/5).3

=4

C-4) arctan1/2+arctan1/3=x olsun.

tanx=tan(arctan1/2+arctan1/3)=

(1/2)+(1/3)

1-(1/2).(1/3)

=1

tanx=1 ise x=45⁰ dir.

C-5) cos(a+b)=cosa.cosb-sina.sinb

arccos12/13=a olsun. cosa=12/13 dir ve dik üçgenden sina=5/13

arcsin8/17=b olsun. sinb=8/17 dir ve dik üçgenden cosb=15/17

cos(arccos12/13 + arcsin8/17) =cos(a+b)=cosa.cosb-sina.sinb=(12/13).(15/17)-(5/13).(8/17)=140/221

[ŞEVVAL58]

sağolun hocam