1.

If tan A – tan B = x and cot B – cot A = y, then the value of cot (A – B) is

Answer»

4) (1/x) + (1/y)

Solution:

GIVEN,

tan A – tan B = x….(i)

cot B – cot A = y

(1/tan B) – (1/tan A) = y

(tan A – tan B)/ (tan A tan B) = y

x/ tan A tan B = y {from (i)}

tan A tan B = x/y….(II)

cot(A – B) = 1/tan(A – B)

= (1 + tan A tan B)/ (tan A – tan B)

= [1 + (x/y)]/ x {from (i) and (ii)}

= (y + x)/xy

= (y/xy) + (x/xy)

= (1/x) + (1/y)


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