Question

If cotA+B=√3 and cotA-B=1...find angle A AND B.
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Answer 1

Answer:

A=37.5   ;   B=7.5

Step-by-step explanation:

→cot(A+B)=√3

But, cot30˚=√3

So,

A+B=30    →  (1)

→cot(A-B)=1

But, cot45˚=1

So,

A-B=45     → (2)

Add (1) and (2)

2A=75˚

∴A=37.5

Subtract (2) from (1)

2B= -15

∴B= -7.5

Answer 2

Answer :-

$A = 37.5^{\circ}$

$B = -7.5^{\circ}$

Given :-

$Cot (A + B) = \sqrt{3}$

$Cot ( A - B) = 1$

To find :-

The value of angle A and B.

Solution:-

→$Cot ( A + B) = \sqrt{3}$

→$Cot ( A + B) = Cot 30^{\circ}$

• Cancelling out Cot on both side.

→$A + B = 30^{\circ}-----1)$

→$Cot (A - B) = 1$

→$Cot ( A -B) = Cot 45^{\circ}$

• Cancelling out Cot.

→$A-B = 45^{\circ}----2)$

• Adding equation.1 and equation 2 we get,

→$A + B + A - B = 30 + 45$

→$2A = 75^{\circ}$

→$A = \dfrac{75}{2}$

→$A = 37.5^{\circ}$

• put the value of A.

→$A + B = 30^{\circ}$

→$37.5 = B = 30$

→$B = 30 - 37.5$

→$B = -7.5^{\circ}$

hence,

The required angle is 37.5° and -7.5°.