Question

tan 37 degree+ tan 45 degree equals to tan x degree then x is

Answer 1

arctan(7/4)

Answer 2

To solve the equation $\tan 37^\circ + \tan 45^\circ = \tan x^\circ$, we need to find the values of $\tan 37^\circ$ and $\tan 45^\circ$.

1. Value of $\tan 45^\circ$: We know that $\tan 45^\circ = 1$.

2. Value of $\tan 37^\circ$: In physics and mathematics problems, especially in competitive exams like JEE and NEET, the angle $37^\circ$ is often approximated using a $3-4-5$ right-angled triangle. In such a triangle:

   • The angle opposite the side of length $3$ is approximately $37^\circ$.
   • The angle opposite the side of length $4$ is approximately $53^\circ$.
   • The hypotenuse is of length $5$.

   For an angle of $37^\circ$, the opposite side is $3$ and the adjacent side is $4$. Therefore, $\tan 37^\circ = \frac{\text{opposite}}{\text{adjacent}} = \frac{3}{4}$.

3. Substitute the values into the equation: The given equation is $\tan 37^\circ + \tan 45^\circ = \tan x^\circ$. Substitute the values we found: $\frac{3}{4} + 1 = \tan x^\circ$

4. Simplify the expression: To add the fractions, find a common denominator: $\frac{3}{4} + \frac{4}{4} = \tan x^\circ$ $\frac{3+4}{4} = \tan x^\circ$ $\frac{7}{4} = \tan x^\circ$

5. Find the value of x: To find $x$, we take the inverse tangent of $\frac{7}{4}$: $x = \arctan\left(\frac{7}{4}\right)$ degrees

This is the exact value of $x$ based on the standard approximation of $37^\circ$. The value $\frac{7}{4} = 1.75$ is slightly greater than $\tan 60^\circ \approx 1.732$, so $x$ is slightly greater than $60^\circ$.