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How do you perform multiplication and use the fundamental identities to simplify #(sinx+cosx)^2#?

Answer 1

# (sinx+cosx)^2 = 1+sin2x #

# (sinx+cosx)^2 = (sinx+cosx)(sinx+cosx) # # " "= sin^2x + 2sinxcosx+cos^2x # # " "= (sin^2x +cos^2x) + 2sinxcosx # # " "= 1+sin2x #

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Answer 2

Jordan Armstrong

To perform multiplication and simplify (sinx + cosx)^2 using fundamental identities, follow these steps:

Expand the expression (sinx + cosx)^2.
Apply the formula for squaring a binomial.
Use trigonometric identities to simplify the expression.

Expanding (sinx + cosx)^2: (sin x + cos x)^2 = (sin x + cos x)(sin x + cos x)

Using the formula for squaring a binomial: = sin^2 x + 2sin x cos x + cos^2 x

Now, apply the fundamental trigonometric identity sin^2 x + cos^2 x = 1: = 1 + 2sin x cos x

So, the simplified expression is: 1 + 2sin x cos 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.