Buktikan identitas berikut : A. Cos A + Tan A = Sec A . Csc A B. ( 1 + Sin A + cos A)² = 2( 1 + sin A)(1+Cos A) C. Cos² A\1-Sin A = 1-Sin A D. 1-Sin A\Cos A + C
Matematika
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Pertanyaan
Buktikan identitas berikut :
A. Cos A + Tan A = Sec A . Csc A
B. ( 1 + Sin A + cos A)² = 2( 1 + sin A)(1+Cos A)
C. Cos² A\1-Sin A = 1-Sin A
D. 1-Sin A\Cos A + Cos A\1-Sin A = 2 Sec A
E. (1-Cos A)(1+Sec A) = Sin A.Tan A
A. Cos A + Tan A = Sec A . Csc A
B. ( 1 + Sin A + cos A)² = 2( 1 + sin A)(1+Cos A)
C. Cos² A\1-Sin A = 1-Sin A
D. 1-Sin A\Cos A + Cos A\1-Sin A = 2 Sec A
E. (1-Cos A)(1+Sec A) = Sin A.Tan A
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Identitas Trigonometri
c.
cos² A /(1 - sin A)
= (1 - sin² A) / (1 - sin A)
= (1 + sin A)(1 - sin A) / (1 - sin A)
= 1 + sin A
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e.
(1 - cos A)(1 + sec A)
= (1 - cos A)(1 + 1/cos A)
= 1(1 + 1/cos A) - cos A (1 + 1/cos A)
= 1 + 1/cos A - cos A - 1
= 1/cos A - cos A
= (1 - cos² A)/cos A
= sin² A / cos A
= sin A . sin A /cos A
= sin A . tan A
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