Sin theta per 1 + cos theta +1 + cos theta per sin theta = 2 per sin theta
Jawaban:
( sin x / 1 + cos x ) + ( 1 + cos x / sin x )
= sin x ( sin x ) + 1 + cos x ( 1 + cos x ) / ( 1 + cos x ) ( sin x )
= sin²x + ( 1 + cos x )² / ( 1 + cos x ) ( sin x )
= sin²x + 1 + 2 cos x + cos²x / ( 1 + cos x ) ( sin x )
= 1 + 1 + 2 cos x / ( 1 + cos x ) ( sin x )
= 2 + 2 cos x / ( 1 + cos x ) ( sin x )
= 2 ( 1 + cos x ) / ( 1 + cos x ) ( sin x )
= 2 / sin x
= 2 csc x
penjelasan
- sin²x + cos²x = 1