Question

if tan(a+b)=√3 and cos(a-b)=√3)2 to find the value a and b​

Answer 1

Step-by-step explanation:

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Answer 2

Given,

tan(a+b)=√3

cos(a-b)=√3/2

To Find,

The value of a and b =?

Solution,

We know that value of tan 60° is √3  and cos 30° is √3/2 from trigonometric table. Therefore,

tan(a+b) = √3  = tan 60°

tan 60° = tan(a+b)

cos(a-b)=√3/2 = cos 30°

cos 30° = cos(a-b)

Equating angles on both sides,

a + b = 60° ⇒ Equation 1

a -  b = 30° ⇒ Equation 2

Adding equation 1 and 2

a + b + a - b = 60° + 30°

2a  = 90°

a = 90 / 2

a = 45°

Putting value of a in equation 1, we get

45 + b = 60°

b = 60° - 45°

b = 15°

Hence, the values of a and b are 45° and 15° respectively.