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son4ous [18]
2 years ago
14

Find the exact value of tan(x-y) if sin x=8/17 cosy = 3/5

Mathematics
1 answer:
jolli1 [7]2 years ago
6 0

To solve the the question we proceed as follows:

From trigonometric laws

(cos x)^2+(sin x)^2=1

(cos x)^2+(sin x)^2=1

sin (x-y)=sin x sin y-sin y cos x

cos (x-y)=cos x cos y+sin x xin y

si  x=\frac{8}{17}

cos x=sqrt(1-(sin x)^2)=sqrt(1-64/289)=sqrt(\frac{225}{289} )=\frac{15}{17}

cos y=\frac{3}{5}

sin x= sqrt(1- (cos x)^2)= sqrt(1-\frac{9}{25} )=sqrt(\frac{16}{25} )=\frac{4}{5}

thus

tan (x-y)=[sin (x-y)]/[cos (x-y)]

=[sin x cos y-sin y cos x]/[cos x cos y+sin x sin y]

plugging in the values we obtain:

[8/17 *3/5-4/5*15/7]/[15/17*3/5+8/17*4/5]

simplifying

[24/85-60/85]/[45/85+32/85]

=-\frac{36}{77}

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