Question

f cos x = 4/5 (x lies in Quadrant IV), then sin x = ​

Answer 1

Answer:

The equation sin x = cos x can also be solved by dividing through by cos x. If we put k = 0 and k = 1 we get the solutions /4 (45°) and /4 + = 5 /4 (45°+ 180°= 225°). To solve the inequality sin x > cos x we need to see which is the greater sin x or cos x on the intervals between the solutions /4 and 5 /4.

Answer 2

Step-by-step explanation:

NSWER

cosx=−

3

1

,π<x<

2

3π

i.e. x lies in 3rd quadrant

Using 1−cosx=2sin

2

2

x

⇒sin

2

x

=±

2

1−cosx

We get, sin

2

x

=±

2

1−(−

3

1

)

=±

6

4

As π<x<

2

3π

⇒

2

π

<

2

x

<

4

3π

and sin is positive in 2nd quadrant

∴sin

2

x

=

5

2

Using 1+cosx=2cos

2

2

x

⇒cos

2

x

=±

2

1+cosx

we get, cos

2

x

=±

2

1+(−

3

1

)

=±

3

1

As π<x<

2

3π

⇒

2

π

<

2

x

<

4

3π

and cos is negative in 2nd quadrant

∴cos

2

x

=−

3

1

Using cosx=

1+tan

2

2

x

1−tan

2

2

x

⇒tan

2

x

=±

1+cosx

1−cosx

We get tan

2

x

=±

1+(−

3

1

)

1−(−

3

1

)

=±

2

As π<x<

2

3π

⇒

2

π

<

2

x

<

4

3π

and tan is negative in 2nd quadrant

∴tan

2

x

=−

2