3 years ago

The figure below shows circle with center O and two perpendicular diameters

1 answer:

3 0

Answer:

Triangles OAB,BOC,COD,DOA are isocele and right , are thus equals and have the same hypothenus . The quadrilater ABCD is a diamond (having 4 sides equals) and its diagonals perpendicular is thus a square.

Step-by-step explanation:

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Sin5A/SinA-cos5A/cosA=4cos2A

irina1246 [14]

Answer:

See Explanation

Step-by-step explanation:

$\frac{ \sin5A}{\sin A} - \frac{ \cos5A}{\cos A} = 4\cos2A \\ \\ LHS = \frac{ \sin5A}{\sin A} - \frac{ \cos5A}{\cos A} \\ \\ = \frac{ \sin5A \:\cos A - \cos5A \: \sin A}{\sin A \:\cos A } \\ \\ = \frac{ \sin(5A -A )}{\sin A \:\cos A} \\ \\ = \frac{ \sin 4A}{\sin A \:\cos A} \\ \\ = \frac{ 2\sin 2A \: \cos 2A}{\sin A \:\cos A} \\ \\ = \frac{ 2 \times 2\sin A \: \cos A \: \cos 2A}{\sin A \:\cos A} \\ \\ = \frac{ 4\sin A \: \cos A \: \cos 2A}{\sin A \:\cos A} \\ \\ =4\cos 2A \\ \\ = RHS \\ \\ thus \\ \\ \frac{ \sin5A}{\sin A} - \frac{ \cos5A}{\cos A} = 4\cos2A \\ \\ hence \: proved$