If sinA=12/13 & tan B=3/4 then find
¡= sin(A+B)
¡¡=COS(A-B)
¡¡¡=COT(A-B)
¡v=cot(A-B)
Sir please give me the correct ans because tomorrow is my class
for sinA = 12/13, we have the 5-12-13 triangle,
so cosA = 5/13
and tanA= 12/5
for tanB = 3/4, we have the 3-4-5 triangle,
so sinB = 3/5
and cosB = 4/5
you have to know the expansion formulas, I will do the first one, you do the rest
sin(A+B) = sinAcosB + cosAsinB
= (12/13)(4/5) + (5/13)(3/5)
= 48/65 + 15/65 = 63/65
always check with a calculator, my answer is correct
I noticed your last two questions are the same, watch for a typo
To find the value of sin(A+B), we can use the trigonometric identity:
sin(A+B) = (sinA * cosB) + (cosA * sinB)
Given that sinA = 12/13 and tanB = 3/4, we can find the values of cosA and sinB using these equations:
cosA = sqrt(1 - sin^2A)
= sqrt(1 - (12/13)^2)
= sqrt(1 - (144/169))
= sqrt(169/169 - 144/169)
= sqrt(25/169)
= 5/13
sinB = tanB / secB
= (3/4) / (1/cosB)
= (3/4) * (4/1)
= 3
Now we can calculate sin(A+B):
sin(A+B) = (sinA * cosB) + (cosA * sinB)
= (12/13) * (3/5) + (5/13) * (3/4)
= (36/65) + (15/52)
= (1872/2600) + (975/2600)
= 2847/2600
= 109/100
Therefore, sin(A+B) = 109/100.
To find the value of cos(A-B), we can use the trigonometric identity:
cos(A-B) = (cosA * cosB) + (sinA * sinB)
Using the previously calculated values of cosA and sinB, we can find cos(A-B):
cos(A-B) = (cosA * cosB) + (sinA * sinB)
= (5/13) * (4/5) + (12/13) * (3/4)
= (20/65) + (36/52)
= (1040/3380) + (702/3380)
= 1742/3380
= 871/1690
Therefore, cos(A-B) = 871/1690.
To find the value of cot(A-B), we can use the trigonometric identity:
cot(A-B) = 1 / tan(A-B)
cot(A-B) = 1 / tan(A-B)
= 1 / ((sin(A-B)) / cos(A-B))
= cos(A-B) / sin(A-B)
= (871/1690) / ((109/100))
= (871/1690) * ((100/109))
= 87100/184610
= 436/923
Therefore, cot(A-B) = 436/923.
Finally, to find the value of cot(A-B), you have repeated the previous question. But based on the calculations above, cot(A-B) = 436/923.
Please note that trigonometric calculations may involve rounding errors, so there might be slight discrepancies in the calculated values.
To find the values of sin(A+B), cos(A-B), cot(A-B), and cot(A-B) using the given information, we will need to use trigonometric identities. Here's how you can find the answers:
Given information:
sin(A) = 12/13
tan(B) = 3/4
1. Finding sin(A+B):
To find sin(A+B), we can use the formula:
sin(A+B) = sin(A)cos(B) + cos(A)sin(B)
To use this formula, we need to find the values of cos(A) and cos(B).
Using the Pythagorean Identity: sin^2(A) + cos^2(A) = 1
Substituting sin(A) = 12/13 into the equation:
(12/13)^2 + cos^2(A) = 1
144/169 + cos^2(A) = 1
cos^2(A) = 1 - 144/169
cos^2(A) = 25/169
cos(A) = √(25/169)
cos(A) = 5/13
Similarly, we can find cos(B) using the Pythagorean Identity:
sin^2(B) + cos^2(B) = 1
Substituting tan(B) = 3/4 into the equation:
(3/4)^2 + cos^2(B) = 1
9/16 + cos^2(B) = 1
cos^2(B) = 1 - 9/16
cos^2(B) = 7/16
cos(B) = √(7/16)
cos(B) = √7/4
Now, substitute the values of sin(A), cos(A), sin(B), and cos(B) into the formula:
sin(A+B) = (12/13)(√7/4) + (5/13)(3/4)
sin(A+B) = (3√7 + 15)/52
So, sin(A+B) = (3√7 + 15)/52
2. Finding cos(A-B):
To find cos(A-B), we can use the formula:
cos(A-B) = cos(A)cos(B) + sin(A)sin(B)
Substitute the values of sin(A), sin(B), cos(A), and cos(B) (calculated above) into the formula:
cos(A-B) = (5/13)(√7/4) + (12/13)(3/4)
cos(A-B) = (15√7 + 12)/52
So, cos(A-B) = (15√7 + 12)/52
3. Finding cot(A-B):
To find cot(A-B), we can use the formula:
cot(A-B) = 1 / tan(A-B)
tan(A-B) can be found using the formula:
tan(A-B) = (tan(A) - tan(B)) / (1 + tan(A)tan(B))
Substitute the values of tan(A) = sin(A)/cos(A) and tan(B) = 3/4 into the formula:
tan(A-B) = [(12/13) - (3/4)] / [1 + (12/13)(3/4)]
tan(A-B) = (48 - 39)/52
tan(A-B) = 9/52
Now, find cot(A-B) by taking the reciprocal:
cot(A-B) = 52/9
So, cot(A-B) = 52/9
4. Finding cot(A-B):
To find cot(A-B) using the reciprocal identity, we can use the formula:
cot(A-B) = 1 / tan(A-B)
Substitute the calculated value of tan(A-B) from step 3:
cot(A-B) = 1 / (9/52)
cot(A-B) = 52/9
So, the final answers are:
¡ = sin(A+B) = (3√7 + 15)/52
¡¡ = cos(A-B) = (15√7 + 12)/52
¡¡¡ = cot(A-B) = 52/9
¡v = cot(A-B) = 52/9