Which sum or difference identity could be used to prove that cos(270degrees-feta)=-sinfeta is an identity?

cos (270° - θ) = -sinθ

Step-by-step explanation:

Explanation:-

Trigonometry sum or difference formula

Cos (A+B) = cos A cos B - sin A sin B

Cos (A+B) = cos A cos B + sin A sin B

Given cos (270° - θ) = cos 270° cosθ + sin 270° sinθ

Cos 270° = cos (180°+90°) = -cos 90° = 0

sin 270°   = sin (180°+90°) = -sin 90° = -1

now

cos (270° - θ) = cos 270° cosθ + sin 270° sinθ

cos (270° - θ) = (0) cosθ + (-1) sinθ = -sinθ

Final answer:-

cos (270° - θ) = -sinθ

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.