Tarea 3. Und 2 - Ejercicios PDF

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Ejercicios ...

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Tarea 3. Revisar y realizar las siguientes identidades trigonométricas 1.

senxsecx =tanx senxsecx =tanx

El

senx .

secx =

1 , reemplazando este valor cos x

1 =tanx cos x

senx =tanx cos x La tan =

senx , por lo tanto cos x

tanx= tanx

2.

(secx+ 1 )( secx−1 ) =tan2 x

(secx+ 1 )( secx−1 ) =tan2 x El producto notable de

a2−b2=( a−b )( a+b ) , aplicando este concepto sec2 x−1= tan2 x

Por la identidad trigonométrica de que 2

2

2

2

sec x=1+ tan x → tan x= sec x−1

Remplazando 2

2

tan x=tan x 3.

cos x csc x=cot x cos x csc x=cot x

El

cscx=

1 , reemplazando este valor sex x

cos x .

1 =cot x sen x

cos x =cot x sen x La csc=

cos x , por lo tanto sen x

csc x=csc x

4.

(1+cos x ) (1−cos x )=sen2 x

(1+cos x ) (1−cos x )=sen2 x El producto notable de

a2−b2=( a−b )( a+b ) , aplicando este concepto 1−cos 2 x=sen2 x

Por la identidad trigonométrica de que 2

2

2

2

sen x +cos x=1 → sen x=1−cos x

Remplazando sen2 x= sen2 x 5.

sec x cot x=csc x sec x cot x=csc x

1 cos x . =csc x cos x sen x 1 1 . =csc x 1 sen x csc x=csc x

6.

2

2

2

2

sen x +3=4 −cos x

sen x +3=4 −cos x

2

2

1−cos x +3=4−cos x 2

2

4 −cos x= 4 −cos x 7.

2

2

2−tan x= 3−sec x

2− tan2 x=3−sec2 x 2 2 2−( sec x −1 ) =3 −sec x

2

2

2−sec x + 1=3−sec x

3−sec2 x =3−sec2 x 8.

cos x =cos2 x sec x cos x =cos2 x sec x cos x =cos2 x 1 cos x cos2 x =cos 2 x 1 2

2

cos x=cos x

9.

csc x 1 = cot x cos x csc x 1 = cot x cos x 1 sen x 1 = cos x cos x sen x sen x 1 = sen x . cos x cos x

1 1 = cos x cos x 10.

cos x tan x +sen x 2 = sec x tan x

2 cos x tan x +sen x = sec x tan x

2 cos x tan x +sen x = sec x tan x

cos x

sen x +sen x cos x 2 = sen x sec x cos x

(sen x +sen x ) cos x 2 = sec x sen x

2 sen x cos x 2 = sec x sen x

2 cos x=

2.

2 sec x

2 1 = sec x sec x

2 2 = sec x sec x

11.

sec x =sen x tan x+ cot x

sec x =sen x tan x+ cot x

1 cos x =sen x sen x cos x + cos x sen x 1 cos x =sen x 2 2 sen x +cos x sen x cos x

sen x cos x

( sen x +cos2 x ) cos x 2

=sen x

sen x =sen x 1

sen x =sen x

12.

cos x =1+sen x sec x−tan x

cos x =1+sen x sec x−tan x

cos x =1+ sen x sen x 1 − cos x cos x

cos x =1+ sen x 1−sen x cos x

cos 2 x =1+ sen x 1−sen x

1−sen2 x =1+sen x 1−sen x

(1−sen x ) (1+ sen x ) =1+ sen x 1−sen x 1 +sen x=1 + sen x

4

13. sen x=

4

sen x=

sen4 x=

4

1−cos 2 x csc2 x 1−cos 2 x csc2 x sen2 x 1 sen2 x 4

sen x= sen x

14.

tan x tan x 2 − = 1+sec x 1−sec x sen x

tan x tan x 2 − = 1+sec x 1−sec x sen x

tan x ( 1−sec x) −tan x ( 1+ sec x ) 2 = sen x ( 1+sec x ) (1−sec x )

tan x [ (1−sec x ) −( 1+ sec x ) ] 2

1−sec x

=

2 sen x

tan x [ 1−sec x−1−sec x] 2 = 2 sen x −tan x

tan x [−2 sec x ] 2

−tan x

=

2 sen x

2 −2 sec x = −tan x sen x

2

1 cos x 2 = sen x sen x cos x

2cos x 2 = sen x cos x sen x

2 2 = sen x sen x...