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Simplify the trig expression. Sin x tan x +cos x.

User Rajeev Varshney
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1 Answer

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Question:

Simplify the trig expression. sin x tan x +cos x.

Solution:

Let the following trigonometric expression:


\sin (x)\tan (x)\text{ + cos(x)}

Rewriting using trigonometric identities:


=\text{ }cos(x)\text{ +}(\sin(x))/(\cos(x))\sin (x)

this is equivalent to:


=\text{ }cos(x)\text{ +}(\sin ^2(x))/(\cos (x))

Converting cos (x) to a fraction, this is equivalent to:


=\text{ }(\cos (x)\cos (x))/(\cos (x))\text{+}(\sin^2(x))/(\cos(x))

Since the denominators are the same, we can combine the fractions:


=\text{ }(\cos (x)\cos (x)+sin^2(x))/(\cos (x))

this is equivalent to:


=\text{ }(\cos ^2(x)+sin^2(x))/(\cos (x))

this is equivalent to:


=\text{ }(1)/(\cos (x))=\text{ }sec(x)

then, we can conclude that the correct answer is :


\sin (x)\tan (x)\text{ + cos(x) = sec(x)}

User LordTribual
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