SOLVING INVERSE TRIGONOMETRIC EQUATIONS USING TAN INVERSE

Solve the following equations for x :

Problem 1 :

tan^-1 2x + tan^-1 3x = nπ + 3π/4

Solution :

So, the solution is x = 1/6.

Problem 2 :

tan^-1 (x+1) + tan^-1 (x-1) = tan^-1 (8/31)

Solution :

So, the value of x is 1/4.

Problem 3 :

Solution :

So, the solution is x = 1.

Problem 4 :

Solution :

So, the value of x is 1/5.

Problem 5 :

Solution :

For what angle measure of tan, we get √3. For tan π/3, we get √3.

So, the value of x is √3.

Problem 6 :

If tan^-1x + tan^-1y = π/4, then write the value of x + y + xy

Solution :

tan^-1x + tan^-1y = π/4

tan^-1(x+y / (1-xy)) = π/4

x + y / (1-xy) = tan π/4

x+y = 1(1-xy)

x + y = 1 - xy

x + y + xy = 1

Problem 7 :

In a triangle ABC, C is a right angle, then

Solution :

Let A, B and C are three interior angles of the triangle.

A= a/(b+c) and B = b/(c+a)

Sum of the interior angles of the triangle is 180 degree.

A + B + C = 180

A + B + 90 = 180

A + B = 90