Question

If tan θ = cot (30° +θ ), find the value of θ.

Answer 1

Two angles are said to be complementary of their sum is equal to 90° .
θ & (90° - θ) are complementary angles

GIVEN:
tan θ = cot (30° + θ )
cot (90° - θ ) =  cot (30° + θ )

[ cot ( 90° - θ) = tan θ ]

90° - θ = 30° + θ
θ + θ = 90 ° - 30 °
θ + θ = 60 °
2 θ = 60°
θ = 60 /2 = 30 °
θ = 30°

Hence , the value of θ is 30°.

HOPE THIS WILL HELP YOU...

Answer 2

tan theeta = tan( 90 - ( 30+ theeta)

Tan theeta = tan(60 - theeta)

tan theeta = tan60 - tan theeta

2 tan theeta = tan 60

tan theeta = 30

= 1/√3...