Question

Theta = pie/19 then find sin23theta- sin 3 theta /sin 16 theta +sin 4 theta

Answer 1

(sin23∅ - sin3∅)/( sin16∅ + sin4∅)
use formula,
sinA + sinB = 2sin(A + B)/2 .cos(A - B)/2
sinA - sinB = 2cos(A + B)/2.sin(A + B)/2

=2cos(23∅ + 3∅)/2.sin(23∅- 3∅)/2/2sin(16∅+4∅)/2.cos(16∅-4∅)/2
= cos13∅.sin10∅/sin10∅.cos6∅
= cos13∅/cos6∅
= cos(13π/19)/cos(6π/19)
= cos( π -6π/19)/cos(6π/19)
= -cos(6π/19)/cos(6π/19)
= -1

Answer 2

Step-by-step explanation:

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