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ozzi
3 years ago
15

Sin(x+y)-sin(x-y)/cos(x+y)+cos(x-y)=tany how do i verify this?

Mathematics
1 answer:
dsp733 years ago
7 0

Answer:

Step-by-step explanation:

Numerator

sin

x

cos

y

+

cos

x

sin

y

−

[

sin

x

cos

y

−

cos

x

sin

y

)

=

sin

x

cos

y

+

cos

x

sin

y

−

sin

x

cos

y

+

cos

x

sin

y

=

2

cos

x

sin

y

Denominator

cos

x

cos

y

−

sin

x

sin

y

+

cos

x

cos

y

+

sin

x

sin

y

=

cos

x

cos

y

−

sin

x

sin

y

+

cos

x

cos

y

+

sin

x

sin

y

=

2

cos

x

cos

y

---------------------------------------------------------------

left side can now be expressed as

2

cos

x

sin

y

2

cos

x

cos

y

=

2

cos

x

sin

y

2

cos

x

cos

y

=

sin

y

cos

y

and  

sin

y

cos

y

=

tan

y

=

right side hence proved

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