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Mathematics
1 November, 10:55
1+sin (a) / 1+csc (a) = tan (a) / sec (a)
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Savannah Coffey
1 November, 11:02
0
Below.
Step-by-step explanation:
(1 + sin a) / (1 + csc a)
= (1 + sin a) / (1 + 1 / sin a)
= (1 + sin a) / (sin a + 1) / (sin a)
= (sin a (1 + sin a)) / (1 + sin a)
= sin a.
tan a / sec a
= (sin a / cos a) / (1 / cos a)
= (sin a cos a) / cos a
= sin a
The two expressions are both equal to sin a:
Therefore
(1 + sin a) / (1 + csc a) = tan a / sec a.
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