Question

tan a+b=1 and cosa-b=root3 /2 then find the value of a and b​

Answer 1

Solution :-

tan ( a + b ) = 1

Also, tan 45° = 1

So, tan (a + b ) = tan 45°

⇒ a + b = 45° → eq ( 1)

cos ( a - b ) = √3 / 2

Also, cos 30° = √3 / 2

So, cos ( a - b ) = cos 30°

⇒ a - b = 30° → eq ( 2)

Adding eq ( 1 ) & eq ( 2 )

⇒ a + b + a - b = 45 + 30

⇒ 2a = 75

⇒ a = 75 / 2

⇒ a = 37.5

Substituting a = 37.5 in eq ( 1)

⇒ 37.5 + b = 45

⇒ b = 45 - 37.5

⇒ b = 7.5

Hence, the value of a is 37.5 and b is 7.5.