The principal value of ⁻¹ ( ( 25 4 ) - ( 25 4 ) ) is equal to

Step-by-step solution

Given expression: ⁻¹ ( ( 25 4 ) - ( 25 4 ) ) First, we simplify the angles using the periodicity of trigonometric functions: 25 4 = 6 + 4 Therefore, (6 + 4 ) = ( 4 ) = 2 (6 + 4 ) = ( 4 ) = 1 Substituting these values into the given expression, we get: ⁻¹( 2 - 1) We know the standard sub-multiple angle value: ( 8 ) = 2 - 1 So the expression becomes: ⁻¹ ( ( 8 ) ) To evaluate this, we convert the tangent function to a cotangent function using the complementary angle identity: ( 8 ) = ( 2 - 8 ) = ( 3 8 ) Now the expres