FIND THE VALUE OF COS X MINUS Y WHEN QUADRANTS ARE MENTIONED

Question 1 :

Find cos(x − y), given that cos x = −4/5 with π < x < 3π/2 and sin y = −24/25 with π < y < 3π/2.

Solution :

Given that, cos x = −4/5 and sin y = −24/25 both are lying in the 3rd quadrant.

So all trigonometric ratios other than tan and cot, we will have negative sign. 

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

cos (x - y)  =  (-4/5)(-7/25) + (-3/5) (-24/25)

  =  (28/125) + (72/125)

  =  (28 + 72)/125

  =  100/125

  =  4/5

Question 2 :

Find sin(x − y), given that sin x = 8/17 with 0 < x < π/2 and cos y = −24/25 with π < y < 3π/2

Solution :

Given that, sin x = 8/17 and cos y = −24/25

Here x lies in the 1^st quadrant and y lies in the 3^rd quadrant.

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

sin (x - y)  =  (8/17) (-24/25) - (15/17) (-7/25)

  =  (-192/425) + (105/425)

  =  (-192 + 105)/425

  =  -87/425

Hence the value of sin (x - y) is -87/425.

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