English, asked by olgachong73, 3 months ago

prove that identity sin 2 A +cos2 A =1​

Answers

Answered by itzHATERxx
0

Answer:

Consider a right angled triangle with an internal angle

θ

:

enter image source here

Then:

sin

θ

=

a

c

cos

θ

=

b

c

So:

sin

2

θ

+

cos

2

θ

=

a

2

c

2

+

b

2

c

2

=

a

2

+

b

2

c

2

By Pythagoras

a

2

+

b

2

=

c

2

, so

a

2

+

b

2

c

2

=

1

So given Pythagoras, that proves the identity for

θ

(

0

,

π

2

)

For angles outside that range we can use:

sin

(

θ

+

π

)

=

sin

(

θ

)

cos

(

θ

+

π

)

=

cos

(

θ

)

sin

(

θ

)

=

sin

(

θ

)

cos

(

θ

)

=

cos

(

θ

)

So for example:

sin

2

(

θ

+

π

)

+

cos

2

(

θ

+

π

)

=

(

sin

θ

)

2

+

(

cos

θ

)

2

=

sin

2

θ

+

cos

2

θ

=

1

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