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Please help me | what is cos^6 x = cot^4*csc^2x-cot^4x????

Please help me | what is cos^6 x = cot^4*csc^2x-cot^4x????-example-1
User Busilinks
by
7.6k points

2 Answers

11 votes

Answer:

so cot^6 (x) =cot^4 (x) csc^2 (x)-cot^4 (x) then you just manipulate the right side cot^4(x)csc^2(x)-cot^4(x) =cot^6(x) which is true

Explanation:

User STT LCU
by
7.7k points
9 votes

Answer:

Write

csc

4

x

as

1

sin

4

x

and

cot

4

x

as

cos

4

x

sin

4

x

csc

4

x

cot

4

x

=

1

sin

4

x

cos

4

x

sin

4

x

=

1

cos

4

x

sin

4

x

Now recall that

a

2

b

2

=

(

a

b

)

(

a

+

b

)

and use this fact with

a

2

being and

b

2

being

cos

4

x

so that

a

is 1 and b is

cos

2

x

So

csc

4

x

cot

4

x

=

1

cos

4

x

sin

4

x

=

(

1

cos

2

x

)

1

+

cos

2

x

sin

4

x

But

cos

2

x

+

sin

2

x

=

1

so that

1

cos

2

x

=

sin

2

x

so

csc

4

x

cot

4

x

=

sin

2

x

1

+

cos

2

x

sin

4

x

=

1

+

cos

2

x

sin

2

x

=

(

1

sin

2

x

)

+

(

cos

2

x

sin

2

x

)

=

c

s

x

2

x

+

cos

2

x

Explanation:

User Joseph Mekwan
by
9.0k points

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