Question

The first three terms in the expansion of In(1 + sin x) in ascending powers of
x are​

Answer 1

Answer:

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Answer 2

Concept:

A series expansion represents a function as a sum of powers in one of its variables or as a sum of powers of another (typically basic) function.

Given:

The term ln(1 + sinx).

Find:

The first three terms are in the expansion of the given term.

Solution:

The expansion of ln(1+x) = $x-\frac{x^{2}}{2}+\frac{x^{3}}{3}-\frac{x^{4}}{4}+\frac{x^{5}}{5}+\cdots$.

Substitute sinx in the place of x in the expansion series.

ln(1+sinx) = $sinx - \frac{sin^2x}{2}+\frac{sin^3x}{3}-\frac{sin^4x}{4}+\cdots$.

Hence, the first three terms in ln(1+sinx) are $sinx, - \frac{sin^2x}{2}, \frac{sin^3x}{3}$.