If tan (A+B)=1 and cos(A-B)=√3/2
Answers
Answered by
6
Answer:-
Given:-
- Tan (A+B)=1
- Cos (A-B)=√3/2
To find:-
- The values of A and B
Solution:-
Tan(A+B)=1----------->(1)
Cos(A-B)=√3/2------------>(2)
From equation (1) tan (A+B)=1
A+B=tan 45°----------(3)
similarly from (3)
A-B=cos 30°----------(4)
So,
A+B=tan 45°
A-B=cos 30° [Here, +B and -B gets cancelled]
--------------------
⇒2A=tan 45°+cos 30°
⇒2A=1+√3/2
⇒A=2+√3/2
⇒A=2+√3/4
From (4)
⇒2+√3/4+B=1
⇒B=1-2+√3/4
⇒B=4-2+√3/4
⇒B=2+√3/4
Answered by
3
Answer:- A= 37.5° , B = 7.5
Step by step explaination:-
tan(A+B)= 1
(A+B) = 45° ----------------[i]
cos (A-B) = √3/2
(A-B)= 30°------------------[ii]
From eq [i] & [ii]
2 A = 45° + 30°
2A = 75°
A = 37.5°
From eq [i] B = 45° - A
B= 45° - 37.5
B= 7.5°
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