Question

if tan(20-3a)=cot(5a-20),than find the value of a

Answer 1

Tan (20 - 3a) = cot (5a - 20)
tan (20-3a) = tan (90 -(5a - 20)
Tan (20 -3a) = tan (110 - 5a)
20 - 3a = 110 -5a
2a = 90
a =45.

Answer 2

tan(20-3a) = cot(5a-20)

tan(20-3a) = tan[90-(5a-30)]

tan(20-3a) = tan(90-5a+20) Therefore,

20-3a = 90-5a+20

90 = 2a

Thus a=90/2

a=45°