Question

if cot (A-B) = √3 and cot (A+B) = √1/3,0° <A+<B<90° , A>B, find 3A +2B​

Answer 1

Answer:

Step-by-step explanation:

Cot(A-B) = √3 ....(1)

We know, Cot 30° = √3

Now, putting the value of √3 in eq. (1)

Cot(A-B) = Cot30°

But equating we get,

A-B = 30°. ...(2)

Now

Cot(A+B) = 1/√3. .....(3)

We know,

Cot 60° = 1/√3

Putting the value of 1/√3 in eq.(3)

Cot(A+B) = Cot60°

By equating

A+B = 60. ...(4)

(2) + (4)

A+B = 60

A-B = 30

——————

2A = 90

A = 45

Putting value of A in eq 2 we get,

B = 15

3A + 2B = 3X45 + 2X15

= 165

Answer 2

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