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asambeis [7]
3 years ago
12

How would you verify the trigonometric identity 2x = 2sinx cosx

Mathematics
2 answers:
ad-work [718]3 years ago
7 0

Answer:

Step-by-step explanation:

2x = 2sinx cosx is not an identity.  An identity is "always true," whereas a conditional equation is true only for specific value(s) of the unknown.  Double check to ensure that you have copied down this problem correctly.

dem82 [27]3 years ago
5 0

Step-by-step explanation:

<em>Hi</em><em>,</em><em> </em><em>there</em><em>!</em><em>!</em>

<em>I</em><em> </em><em>hope</em><em> </em><em>you</em><em> </em><em>mean</em><em> </em><em>sin2x</em><em>=</em><em>2</em><em>sinx</em><em> </em><em>.</em><em> </em><em>cosx</em>

<em>so</em><em>,</em><em> </em><em>let's</em><em> </em><em>begin</em><em> </em><em>in</em><em> </em><em>a</em><em> </em><em>simple</em><em> </em><em>way</em><em>;</em><em> </em><em>by</em><em> </em><em>adding</em><em>,</em><em> </em><em>alright</em><em>:</em>

<em>sin2x</em><em>=</em><em> </em><em>sin</em><em>(</em><em>x</em><em>+</em><em>x</em><em>)</em><em> </em><em> </em><em> </em><em> </em><em> </em><em>(</em><em>as</em><em> </em><em>2</em><em>x</em><em>=</em><em>x</em><em>+</em><em>x</em><em>)</em><em>.</em>

<em>now</em><em>,</em><em> </em><em>let's</em><em> </em><em>use</em><em> </em><em>compound</em><em> </em><em>formula</em><em> </em><em>for</em><em> </em><em>sin</em><em>,</em>

<em>so</em><em>,</em><em> </em><em>we</em><em> </em><em>get</em><em>:</em>

<em>sin</em><em> </em><em>(</em><em>x</em><em>+</em><em>x</em><em>)</em><em>=</em><em> </em><em>sinx.cosx</em><em> </em><em>+</em><em> </em><em>cosx</em><em>.</em><em> </em><em>sinx</em><em> </em><em> </em><em> </em><em>(</em><em>as</em><em> </em><em>sin</em><em>(</em><em>A</em><em>+</em><em>B</em><em>)</em><em>=</em><em>sin</em><em> </em><em>A</em><em>.</em><em> </em><em>cosB</em><em> </em><em>+</em><em> </em><em>cosA</em><em> </em><em>.</em><em> </em><em>sinB</em><em>)</em>

<em>or</em><em>,</em><em> </em><em>sin</em><em> </em><em>(</em><em>x</em><em>+</em><em>x</em><em>)</em><em>=</em><em>2</em><em>sinx</em><em>.</em><em>cosx</em><em> </em><em> </em><em>(</em><em>adding</em><em> </em><em>both</em><em>)</em><em>.</em>

<em>Therefore</em><em>, </em><em> </em><em>sin</em><em> </em><em>2</em><em>x</em><em> </em><em>=</em><em> </em><em>2sinx</em><em>.</em><em> </em><em>cosx</em><em>.</em>

<em><u>Hope</u></em><em><u> </u></em><em><u>it helps</u></em><em><u>.</u></em><em><u>.</u></em>

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