Question

SinA-cosB=7/5 ,0* < x < 180* nilai sin A+cos B =

Answer 1

Verified answer

Trigonometri

Rumus jumlah dan selisih sudut

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sin  A - cos B =  7/5

(sn A - cos B)² = (7/5)²

sin² A - 2 sin A cos B + cos² B = (49/25)

(sin² A + cos ² A )  - 2 sin A cos A = 49/25)

1 - 2 sin A cos A = 49/25

2 sin A cos A = 1 - 49/25

2 sin A cos A = - 24/25 ...(1)

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misal

P = sin A + cos A  

P² = (sin A + cos A)² = sin² A + 2 sinA cos A + cos²A

P² = (sin² A + cos² A)  + 2 sin A cos A

P²  =  1 + 2 sin A cos A

P² = 1 + (-24/25)

P² = 1 - 24/25 = 1/25

p = 1/5  atau p= - 1/5

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Maka

sin A + cos A =  1/5   atau sin A + cos A = - 1/5