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How do you solve: (1+sinx)(1+sin(-x)) ?

Answer 1

Oliver Atkinson

Please see below.

If you meant how do you simplify this:

#(1+sinx)(1+sin(-x))=(1+sinx)(1-sinx)=1-sin^2x=cos^2x#

If you meant to solve for #x# by setting it equal to #0#:

Within one period of #0 < x < 2pi#

#cos^2x=0, :. cosx=0, :. x=pi/2, (3pi)/2#

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Answer 2

Violet Anderson

To solve the expression (1+sinx)(1+sin(-x)), we'll use the trigonometric identity sin(-x) = -sinx. Substitute sin(-x) with -sinx:

(1+sinx)(1-sinx)

Now, we'll use the difference of squares formula, a^2 - b^2 = (a+b)(a-b):

1^2 - (sinx)^2

This simplifies to:

1 - sin^2(x)

Using the Pythagorean identity sin^2(x) + cos^2(x) = 1, we get:

1 - (1 - cos^2(x))

Simplify this expression:

cos^2(x)

Therefore, (1+sinx)(1+sin(-x)) simplifies to cos^2(x).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.