Math, asked by aryansharmaatm, 7 months ago

cos x +cos y =b ,sin x +sin y=a , then prove that cos (x-y)=1/2(a²+b²-2)​

Answers

Answered by yogesh9836
0

Answer:

Given that,

cos

x

+

c

o

y

=

a

....[1]

sin

x

+

sin

y

=

b

....[2]

Squaring and adding [1] and [2], we get,

cos

2

x

+

2

cos

x

cos

y

+

cos

2

y

+

sin

2

x

+

2

sin

x

sin

y

+

sin

2

y

=

a

2

+

b

2

2

+

2

(

cos

x

cos

y

+

sin

x

sin

y

)

=

a

2

+

b

2

2

(

1

+

cos

(

x

y

)

)

=

a

2

+

b

2

cos

(

x

y

)

=

a

2

+

b

2

2

1

Dividing equation [1] by [2], we get,

cos

x

+

cos

y

sin

x

+

sin

y

=

a

b

2

cos

(

x

+

y

2

)

cos

(

x

y

2

)

2

sin

(

x

+

y

2

)

cos

(

x

y

2

)

=

a

b

cot

(

x

+

y

2

)

=

a

b

tan

(

x

+

y

2

)

=

b

a

x

+

y

2

=

tan

1

(

b

a

)

Step-by-step explanation:

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