Question 986288: If tan theta=cot<60`+theta> find the value of theta
tanΘ = cot(60 + Θ) , Find the value of Θ
Answer by sanusi hammed (1)   (Show Source):
You can put this solution on YOUR website! If tan theta=cot<60`+theta> find the value of theta
SOLUTION
tanΘ = cot(60 + Θ) , Find the value of Θ
Note: tanΘ = sinΘ/cosΘ
And Also Note: cotΘ = cosΘ/sinΘ
Hence, tanΘ = cot(60 + Θ)
∴(sinΘ/cosΘ) = [cos(60 + Θ)/sin(60 + Θ)]
By equating numerator with numerator and denominator with denominator, we get. .
∴ sinΘ = cos(60 + Θ)
From trigonometry identity:sinΘ = cos(90 - Θ)
By comparing the equation, we got. ..
cos(60 + Θ) = cos(90 - Θ)
Council out cos, we will get
∴ 60 + Θ = 90 - Θ
Collect the like term
∴ Θ + Θ = 90 - 60
∴ 2Θ = 30
Divide both side by 2
∴ Θ = 30/2
∴ Θ = 15 °
By equating the denominator, we will have
CosΘ = sin(60 + Θ)
From trigonometry identity: cosΘ = sin(90 - Θ)
By comparing the equation, we get
sin(60 + Θ) = sin(90 - Θ)
Cos will council out, we get
60 + Θ = 90 - Θ
Collect the like term
∴ Θ + Θ = 90 - 60
∴ 2Θ = 30
Divide both side by 2
∴ Θ = 30/2
∴ Θ = 15 °
Therefore the value of theta , Θ = 15°
Checking:
tanΘ = cot(60 + Θ)
tan15° = cot(60 + 15°)
tan15° = cot75°
Note: cotΘ = 1/tanΘ
tan15° = 1/tan75°
0.267949192 = 1/(3.732050808)
0.267949192 = 0.267949192
Therefore, the value of theta , Θ = 15°
|
|
|
