8. a. Verify the given identity: sec(0)- cos(0) = sin(0))tan(0) b. Use part a to solve the equation: sec(0)-cos(0)+sin(0)=0. Let k be any integer.

Given sec(a) = 5/2 and sin(b) = -1/4, and a and b are both in the interval [(3pi)/2, 2pi). Without solving for a and b, find exact value of sin(a+b)

For the constant numbers a and b, use the substitution x = a cos² u + b sin² u, for 0 < u < , to show that s dx √(x − a)(b − x) - = 2arctan X √b-x a + c₂ (a < x < b) Hint. At some point, you may need to use the trigonometric identities to express sin² u and cos² u in terms of tan² u.

Find the value of R in the following expression: a. cos(0) + b. sin(0) = R cos(0 + a) for a 7 b -3.3 Give your answer to 2 decimal places.