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if sin x=3/5 , cos y= -12/13 and x,y both lie in the second quadrant find the value of:- (a) cos(x-y) (b) tan(x+y)

if sin x=3/5 , cos y= -12/13 and x,y both lie in the second quadrant find the value of:- 
(a) cos(x-y)
(b) tan(x+y) 

Grade:11

1 Answers

Snehal Jadhav
54 Points
5 years ago
We, are given information that both sin(x) and cos(y) lie in second quadrant.
By that we can say that sin will be positive and cos will be negative.
sin(x)=3/5
cos(x)=(1 – sin2(x))1/2
cos(x)=+(or) – 4/5
Since,(x) is in 2nd quadrant, cos(x) will – 4/5
cos(x – y) = cos(x)cos(y) + sin(x)sin(y)
Similarly, sin(y)=5/13.
By, applying the above formula we get:
cos(x-y) = (-)4/5*(-)12/13 + 3/5*5/13
              = 63/65 
For, the second part we would be using the given below formula:
tan(x+y) = (tan(x) + tan(y)) ÷ (1 – tan(x)tan(y))
tan(x)=3/5    &    tan(y)=5/12
tan(x+y) = [3/5 + 5/12]÷[1 – 3/5×5/12]
              = 61/45

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