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vivado [14]
3 years ago
10

Question 16 (Essay Worth 7 points) Verify the identity. tan (x + π/2) = -cot x

Mathematics
1 answer:
Rus_ich [418]3 years ago
6 0

Step-by-step explanation:

We know that tan=sin/cos, so tan(x+π/2)=

\frac{sin(x+pi/2)}{cos(x+pi/2)}

Then, we know that sin(u+v)=sin(u)cos(v)+cos(u)sin(v),

so our equation is then

\frac{sin(x)cos(\pi/2)+cos(x)sin(\pi/2)}{cos(x+\pi/2)}  = \frac{cos(x)}{cos(x+\pi/2) }

Then, cos(u+v)=cos(u)cos(v)-sin(u)sin(v), so our expression is then

\frac{cos(x)}{cos(x)cos(\pi/2)-sin(x)sin(\pi/2)} = \frac{cos(x)}{-sin(x)} = -cot(x)

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Given:

Consider the below figure attached with this question.

In circle A below, chord BC and diameter DAE intersect at F.

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According to intersecting chords theorem, if two chords intersect inside the circle then the angle on the intersection is the average of intercepted arcs.

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