Explanation

The sine function, f(x) = sin(x), is an odd function because it has the property: f(-x) = -f(x).

Explanation

• If the angle is between 0 to 90 degrees then it will lies in the first quadrant.
• The tanθ and sinθ have positive values, hence lies in first quadrant.

Explanation

If * is a binary operation in A, then it means that for all elements a, b in A, the result of the operation a * b is also an element in A. This is the definition of closure under a binary operation.

Explanation

Sin(n+a) = -sina

Explanation

The distributive property of set operations states that:

A × (B ∪ C) = (A × B) ∪ (A × C)

Explanation

Explanation

The sum-to-product identity for cosine states that:

cos(θ) + cos(n) = 2cos((θ+n)/2)cos((θ-n)/2)

This is a fundamental identity in trigonometry, and it is used to simplify expressions involving sums of cosine functions.

Explanation

Anaesthetize is the correct spelt word.

Explanation

A siesta is a short nap or period of rest taken in the early afternoon, typically after lunch.

Explanation

The sentence "They will have been writing their letters" is in the Future Perfect Continuous tense, which is used to describe an action that will be in progress at a specific point in the future and will have started before that point.