If tanA=15/8 and tanB=7/24, then what is cos(A+B)?
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Answered by
0
Answer:
See, cos(A + B) is basically cosAcosB - sinAsinB
So, if tan(A) = 15/8, then clearly sin(A) = 15/17, cos(A) = 8/17
Also, tan(B) = 7/24, so clearly sin(B) = 7/25 and cos(B) = 24/25
These are from simple trigonometric identities.
Then, cos(A+B) = (192 - 105)/425
Which makes it 87 / 425.
Answered by
1
Answer:
tanA=15/8
p/b=15/8
so,h=
=
=
=17
here,sinA=p/h=15/17
cosA=b/h=8/17
tanB=7/24
p/b=7/24
so,h=\sqrt{p^{2} +b^{2}
=
=
=25
here,sinB=p/h=7/25
cosB=b/h=24/25
Now,cos(A+B)=cosAcosB-sinAsinB
=8/17+24/25-(15/17+7/25)
=114/425
Step-by-step explanation:
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