Question

if tan (theta+37°) = cot theta ; 0≤theta≤90° , find the value of theta

Answer 1

Step-by-step explanation:

value of theta is 53 degree

Answer 2

Given:

$\tan (\theta+37)$ = $\cot \theta$

Where, 0° ≤ θ ≤ 90°

We have to find, the value of θ is:

Solution:

∴ $\tan (\theta+37)$ = $\cot \theta$

Using the trigonometric identity:

$\cot \theta$ = $\tan (90-\theta)$

$\tan (\theta+37)$ = $\tan (90-\theta)$

⇒ θ + 37° = 90° - θ

⇒ θ + θ = 90° - 37°

⇒ 2θ = 53°

⇒ θ = $\dfrac{53}{2}$

⇒ θ = 26.5°

Thus, the value of "θ is 26.5°".