Question

If tan 3a = cot (a-26), 3a <90°, find value of angle a

Answer 1

Tan 3a=cot(a-26)
Cot(90-3a)=cot(a-26)
90-3a=a-26
4a=64
a=16
Hence angle a=16 degree

Answer 2

tan 3a = cot ( a - 26 )

Also,

tan∅ = cot ( 90 - ∅ )

So,

tan3a = cot ( 90 - ( a - 26 ) )

tan3a = cot ( 90 - a + 26 )

tan3a = tan ( 64 - a )

( dividing both side by tan that is cancelling tan )


3a = 64 - a

3a + a = 64

4a = 64

a = 16