Question

If tan (A+B)=1 and cos(A-B)=√3/2

Answer 1

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

Answer 2

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°