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sena∗cosβ+ senβ∗cosa sen a+cos a=1 sen β+cos β =1 a=1 sen β+

1) Trigonometric identities are used to relate sin(a+b) to sin(a)cos(b) and sin(b)cos(a). 2) Using trigonometric angle addition identities and Pythagorean identities, expressions for cos(a) and sin(b) are derived in terms of square roots. 3) The expressions are substituted back into the original expression relating sin(a+b) to sin(a)cos(b) and sin(b)cos(a) to obtain the final simplified expression.

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Victor Agramonte
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63 views1 page

sena∗cosβ+ senβ∗cosa sen a+cos a=1 sen β+cos β =1 a=1 sen β+

1) Trigonometric identities are used to relate sin(a+b) to sin(a)cos(b) and sin(b)cos(a). 2) Using trigonometric angle addition identities and Pythagorean identities, expressions for cos(a) and sin(b) are derived in terms of square roots. 3) The expressions are substituted back into the original expression relating sin(a+b) to sin(a)cos(b) and sin(b)cos(a) to obtain the final simplified expression.

Uploaded by

Victor Agramonte
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
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7)

sin( a+ β ¿)=sena∗cosβ+ senβ∗cosa ¿

sen2 a+cos 2 a=1 sen2 β+cos 2 β =1

3 2 1 2
()
5
+cos 2 a=1 sen2 β+ ()
4
=1

2 2
3 1
cos 2 a=1− ()
5
sen2 β=1− ()
4

9 1
cos 2 a=1− sen2 β=1−
25 16
25−9
cos 2 a=
25
16−1
sen2 β=
16
16
cos 2 a=
25
15
sen2 β=
16

16 √ 16 4
cos a=
√= =
25 √ 25 5
15 √ 15 √ 15
senβ=
√=
16 √ 16
=
4
sin( a+ β ¿)=sena∗cosβ+ senβ∗cosa ¿
3 √ 15
∗1 ∗4
5 4
sin( a+ β ¿ )= + ¿
4 5
3 4 √ 15 3+4 √ 15
sin( a+ β ¿)= + = ¿
20 20 20

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