Use trig identities to calculate sin(2x) and cos(2x) based on given information tanx=2 and cosx>0

Find sin 2x, knowing tan x = -2, and cos x > 0

Ans:

sin

2

x

=

4

5

Explanation:

3 Trig identities to be used:

1

+

tan

2

x

=

1

cos

2

x

(1)

sin

2

x

+

cos

2

x

=

1

(2)

sin

2

x

=

2

sin

x

.

cos

x

(3)

Given tan x = -2. First find cos x and sin x

(1) -->

1

+

4

=

1

cos

2

x

-->

cos

2

x

=

1

5

-->

cos

x

=

±

1

√

5

.

Since cos x > 0, then

cos

x

=

1

√

5

.

(2) -->

sin

2

x

=

1

−

cos

2

x

=

1

−

1

5

=

4

5

-->

sin

x

=

±

2

√

5

.

Since cos x > 0 then

sin

x

=

2

√

5

.

(3) -->

sin

2

x

=

2

sin

x

.

cos

x

=

2

(

1

√

5

)

(

2

√

5

)

=

4

5

Answer link

step-by-step explanation:

i have done this all on a piece of paper but idk how to put it on here cuz it needs to be drawn