sin^2(-0)-sec^2(-0)+cos^2(-0)

Question

write each expression in terms of sine and cosine, and simplify so that no quotients appear in the final expression and all functions are 0 only. 0 meaning theta

Answer 1

sin²0 - (1/(cos²0)) + cos²0

 

Now we have an expression in terms of sine and cosine. Let's rewrite the expression so that we have no denominators when we simply.

 

(cos²0 sin²0 - 1 + cos⁴0) / cos²0 =

 

(cos²0 (1 - cos²0) - 1 + cos⁴0) / cos² =

 

(cos²0 - cos⁴0 - 1 + cos⁴0) / cos² =

 

(cos²0 - 1) / sin²0 =

 

(cos0 + 1)(cos0 - 1)(cos^-20)

 

 

 

 

Answer 2

sin² (θ) - sec²(θ) + cos²(θ) = (1 - cos²(θ)) - sec²(θ) + cos²(θ)

 

                                      = 1 - sec²(θ)

 

                                      = -tan²(θ)