Question

If tan theta= cot (30+theta) , then value of theta is?

Answer 1

Given, tan theta= cot (30+theta)  can be written as,

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

             tan theta = tan(90 - 30 - theta)

             theta = tan 60 - theta

              theta + theta =  60

                 theta = 60/2

                  theta = 30.



Hope this helps!

Answer 2

Concept:

The study of specific functions of angles and how to apply them to computations is the subject of trigonometry, a branch of mathematics. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

Given:

It is given that $\tan \theta=\cot(30+\theta)$.

Find:

We need to determine the worth of $\theta.$

Solution:

The trigonometric functions, which are actual functions, connect a right-angled triangle's angle to the ratios of its two side lengths.

Due to that $\tan \theta=\cot(30+\theta)$.

At this point, we'll use the formula $\tan \theta=\cot (90-\theta)$, we get

$\cot (90-\theta)=\cot (30+\theta)$

Additionally, we obtain $\cot$ from both sides, we get

$90-\theta=30+\theta\\90-30=2\theta\\60=2\theta\\30=\theta$

Hence, the value of $\theta$ is $30^{\circ}$.

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