1.

( cos x - sin x )^ 2 = 1- sin 2 x​

Answer»

Answer:

It depends on how far back you need to go in your proof.

If you can use:

sin

2

(

x

)

+

COS

2

(

x

)

=

1

(which can be derived from the Pythagorean Theorem)

and

sin

(

2

x

)

=

2

sin

(

x

)

⋅

cos

(

x

)

(the Double Angle FORMULA for sin, which is considerably more complicate to prove)

then the REQUESTED proof is fairly SIMPLE:

(

sin

(

x

)

+

cos

(

x

)

)

2

=

sin

2

(

x

)

+

2

sin

(

x

)

⋅

cos

(

x

)

+

cos

2

(

x

)

=

[

sin

2

(

x

)

+

cos

2

(

x

)

]

+

2

sin

(

x

)

⋅

cos

(

x

)

=

1

+

sin

(

2

x

)


Discussion

No Comment Found

Related InterviewSolutions