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3 years ago

9

For the following relation, find the: a) Reflexive closure b) Symmetric closure c) Transitive closure 2 You may include explanat

ion if you like but no explanation is required. Your solution may be a graphical representation.v g

1 answer:

Luba_88 [7]3 years ago

5 0

Answer:

Following are the complete solution in the attached file.

Step-by-step explanation:

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Tan(A+45°) - tan(A-45°) =2sec2A

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$\tan(A + 45 \degree) - \tan(A - 45 \degree) \\ \\ = \frac{ \tan(A) + \tan(45 \degree) }{1 - \tan(A) \tan(45 \degree) } - \frac{ \tan(A) - \tan(45 \degree) }{1 + \tan(A) \tan(45 \degree) } \\ \\$

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$= \frac{ \tan(A) }{1 - \tan(A) } - \frac{ \tan(A) }{1 + \tan(A) } \\ \\ \frac{\tan(A) + { \tan }^{3} A + \tan(A) - { \tan}^{3} A}{1 - { \tan }^{2} A } \\ \\ = (\frac{2 \tan(A) }{1 - { \tan }^{2} A}) \\ \\ = \frac{2 \sin(A) }{ \cos(A) } \times { \sec }^{2} A \\ \\ = \frac{2}{ \cos(2A) } \\ \\ = 2 \sec(2A)$

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