Question

prove that : mod root 1-sin/root 1+sin + root1+sin/root 1-sin = -2/cos , where pie/2< theta

Answer 1

sinx=

2

tanx

2

 

1+

tan2x

2

 

 

cosx=

1-

tan2x

2

 

1+

tan2x

2

 

 

y=

√

(1+

2

tanx

2

 

1+

tan2x

2

 

 

1-

tan2x

2

 

1+

tan2x

2

 

 

 

)

y=

1+

tanx

2

 

√

1-

tan2x

2

 

 

y=

1-

tanx

2

 

√

1-tan2x

 

I=∫

π

4

 

0

√

1+sinx

cosx

 

-

√

1-sinx

cosx

 

dx

I=∫

π

4

 

0

2tan(

x

2

 

)

√

1-

tan2x

2

 

 

dx

I=∫

√

2

-1

0

2t2dt

√

1-t2

(1+t2)

 

I=∫

√

2

-1

0

4dt

(1+t2)

√

1-t2

 

option b is corect.