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Fittoniya [83]
2 years ago
11

0%7D%20%20%3D%20%20%5Csin%28x%29%20" id="TexFormula1" title=" \frac{ \sin(x) + \tan(x) }{1 + \sec(x) } = \sin(x) " alt=" \frac{ \sin(x) + \tan(x) }{1 + \sec(x) } = \sin(x) " align="absmiddle" class="latex-formula">
how do I verify this problem?​
Mathematics
1 answer:
GrogVix [38]2 years ago
6 0

Answer:

see explanation

Step-by-step explanation:

Consider the left side

Simplify the numerator/denominator using the trigonometric identities

• tanx = \frac{sinx}{cosx} and secx = \frac{1}{cosx}

sinx + tanx = sinx + \frac{sinx}{cosx} = \frac{xsinxcosx+sinx}{cosx}

= \frac{sinx(1+cosx)}{cosx} ← numerator

and

1 + secx = 1 + \frac{1}{cosx} = \frac{cosx+1}{cosx} ← denominator

Putting this together gives

\frac{sinx(1+cosx)}{cosx} × \frac{cosx}{1+cosx}

Cancel cosx and (1 + cosx) on numerator/ denominator, leaving

left side = sinx = right side ⇒ verified

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