Question

If a and b are acute angles such that tan (a+b)= 1.73 and tan(a-b) =1/1.73, find a and b

Answer 1

`\LARGE{ \underline{ \boxed{ \orange{ \rm{Solution:)}}}}}`

Given,

• tan (a + b) = 1.73
  `\approx` √3
• tan (a - b) = 1 / 1.83
  `\approx` 1 / √3

To find:

• Value of a and b in degrees....?

Solution:

☃️ Refer to the trigonometric table....

Then, proceeding

⇛ tan 60 ° = √3

⇛ tan 60° = tan (a + b)

⇛ 60° = a + b

Flipping it,

⇛ a + b = 60° --------(1)

And,

⇛ tan 30° = 1 / √3

⇛ tan 30° = tan (a - b)

⇛ 30° = a - b

Flipping it,

⇛ a - b = 30° ---------(2)

Now adding eq.(1) and eq.(2),

⇛ a + b + a - b = 60° + 30°

⇛ 2a = 90°

⇛ a = 90° / 2

⇛ a = 45°

Putting value of a in eq.(1),

⇛ 45° + b = 60°

⇛ b = 15°

☄ So, Our Required answers:

• a = 45°
• b = 15°

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