Question

Write the given algebraic expression as a function of θ, where ( 0<θ<π/2}, by making the given substitution. ( √(x+5)^{2}-4} . Substitute x=2 sec θ-5

a -2 tan θ
b. 4 tan θ
c. 4 cot θ
d- 2cot θ

Answer 1

The given algebraic expression, when substituted with x=2secθ-5a-2tanθ, can be written as a function of θ as 2secθ-5a-2tanθ+1.

Step-by-step explanation:

The given algebraic expression is √((x+5)^2)-4. We are asked to substitute x=2secθ-5a-2tanθ into the expression.

1. First, substitute x=2secθ-5a-2tanθ into the expression:
   √(((2secθ-5a-2tanθ)+5)^2)-4
2. Simplify the expression:
   √((2secθ-5a-2tanθ+5)^2)-4
3. Expand the square:
   (2secθ-5a-2tanθ+5)-4
4. Simplify:
   2secθ-5a-2tanθ+1

Therefore, the given algebraic expression, when substituted with x=2secθ-5a-2tanθ, can be written as a function of θ as 2secθ-5a-2tanθ+1.