7. Given the following identity, sec xcscx ftanx+ cot x)-2+tan x+ cot x: Prove the identity by completing the table below, indicating the steps on the left and the reasoning on the right. (12 points) Calculation Reason sec x cscx(tanx+ cot x) Given in the problem Apply the distributive property Apply the definitions of secant, cosecant, tangent, and cotangent Simplify the expressions Apply the definitions of secant and cosecant Apply the Pythagorean identities Simplify the expressions 8. Use the sum identity for tangent to find the exact value of tan Part I: Find two common angles that sum to 12 (2 points) Part II: Evaluate the expression using the sum identity for tangent. (4 points) 9. Consider the vector v = (-6,13). Part I: Use the dot product to find the angle (in degrees) between v = (-6,13) and the vector (1,0). (4 points) Part II: Writev in the form (I v|cosej v| sine). Express the angle e in degrees. (4 points) Part IlI: Use the dot product of the vectors V- (-6,13) and w- (-42,-34) to determine if they are orthogonal. (2 points) 10. Find the fourth roots of the complex number z, - 1+ 3 1. Part I: Write z, in polar form. (2 points) Part II: Find the modulus of the roots of z1. (2 points) Part IlI: Find the four angles that define the fourth roots of the number z1. (4 points) Part IV: What are the fourth roots of z, = 1+ 31? (4 points) %3D