Math, asked by shiyamehta120, 7 months ago

if tan x = 3/4,π<x<3x/2, find the value of sin x/2 ,cos x/2and tan x /2​

Answers

Answered by rajeshbhu555
0

Step-by-step explanation:

Given

π

<

x

<

3

π

2

and

tan

x

=

3

4

π

<

x

<

3

π

2

π

2

<

x

2

<

3

π

4

x

2

2nd quadrant

This means

sin

(

x

2

)

+

v

e

cos

(

x

2

)

v

e

tan

(

x

2

)

v

e

Now

tan

x

=

3

4

2

tan

(

x

2

)

1

tan

2

(

x

2

)

=

3

4

8

tan

(

x

2

)

=

3

3

tan

2

(

x

2

)

3

tan

2

(

x

2

)

+

8

tan

(

x

2

)

3

=

0

3

tan

2

(

x

2

)

+

9

tan

(

x

2

)

tan

(

x

2

)

3

=

0

3

tan

(

x

2

)

(

tan

(

x

2

)

+

3

)

1

(

tan

(

x

2

)

+

3

)

=

0

(

3

tan

(

x

2

)

1

)

(

tan

(

x

2

)

+

3

)

=

0

This means

tan

(

x

2

)

=

1

3

not acceptable as

tan

(

x

2

)

v

e

So

tan

(

x

2

)

3

Now

cos

(

x

2

)

=

1

sec

(

x

2

)

=

1

1

+

tan

2

(

x

2

)

=

1

1

+

(

3

)

2

=

1

10

Again

sin

(

x

2

)

=

tan

(

x

2

)

×

cos

(

x

2

)

=

3

×

(

1

10

)

=

3

10

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