Simplify the expression (cosx - sinx) (1+4 sinxcosx)

sin3x - cos3x

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sin3x + cos3x

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sinx - cosx

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sin2x - cos2x

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Solution

The correct option is B
sin3x + cos3x

(cosx - sinx) (1 + 4 sinx.cosx)

$c o s x + 4 s i n x c o s^{2} x - s i n x - 4 s i n^{2} x c o s x$

Option are in terms of trigonometric ratios of 3x and 2x.

We should further simplify the above given expression.By using identity $s i n^{2} x + c o s^{2} x = 1$

= $c o s x + 4 s i n x (1 - s i n^{2} x) - s i n x - 4 (1 - c o s^{2} x) c o s x$

$c o s x + 4 s i n x - 4 s i n^{3} x - s i n x - 4 c o s x + 4 c o s^{3} x$

= $3 s i n x + 4 s i n^{3} x + 4 c o s^{3} x - 3 c o s x$

= sin3x + cos3x

Suggest Corrections

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