Question

if cos (x-y)=-1,then cosx+cosy


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Answer 1

Answer:

Step-by-step explanation:

cos(x-y)=-1

cos(x-y)=cosπ

(because cos 180 i.e,π=-1 value)

therefore,

cos(x-y)=cos π

(cos will be cancelled)

x-y=π

x=π+y (cos is negative in quadrant 3 , cos 180- theta= cos theta)

-cos y+ cos y

=0

Answer 2

Concept

Recall some values which will use to solve

1. cos(π+A) = -cos(π)

Given

The value of cos(x-y) = -1

To Find

The value of cosx+cosy

Solution

Let cos( x - y ) = -1 ..... (1)

we know that cosπ = -1  ..... (2)

So by comparing both the equation (1) and (2)

we get

cos(x-y) = cosπ

x - y = π

x = π + y

Now, find the value of cosx + cosy.

Substituting the value of x

cos(π+y)+cosy = -cosy+cosy

                      = 0

Hence, the value of cosx+cosy is 0.