Buktikan! cos A - sin²A = cos A + sin A 1-tan A cos A-sin A
Matematika
luna1328
Pertanyaan
Buktikan!
cos A - sin²A = cos A + sin A
1-tan A cos A-sin A
cos A - sin²A = cos A + sin A
1-tan A cos A-sin A
1 Jawaban
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1. Jawaban Lenasutanti
1) Left side = {(1/sinA) - sin A}*{(1/cos A) - cos A}
2) Taking LCM and simplifying, left side = {(1 - sin²A)/sin A}*{(1 - cos²A)/cos A}
= (cos²A/sin A)*(sin²A/cos A) = (sin A)(cos A)/1
3) Since 1 = sin²A + cos²A, by trigonometric identity,
Left side = {(sin A)*(cos A)}/(sin²A + cos²A)
Dividing numerator and denominator by {sin A)*(cos A)} in the above,
Left side = 1/[{sin²A/(sin A*cos A)} + {cos²A/(sin A* cos A)}]
This simplifies to:
1/[(sin A/cos A) + cosA /sin A)] = 1/[tan(A) + cot(A)] = Right side [Proved]