Math, asked by burhansahir, 5 hours ago

Sec²x- tan²x=1-sinx/1+sinx​

Answers

Answered by sunprince0000
1

Answer

Given: y=tanx+secx

Prove that:  

dx  

2

 

d  

2

y

=  

(1−sinx)  

2

 

cosx

 

y=  

cosx

sinx

+  

cosx

1

 

=  

cosx

1+sinx

 

differentiate with respect to x

dx

dy

=  

dx

d

(  

cosx

1+sinx

)

dx

dy

=  

cos  

2

x

cosx  

dx

d

(1+sinx)−(1+sinx)  

dx

d

cosx

 

=  

cos  

2

x

cos  

2

x+sinx+sin  

2

x

=  

cos  

2

x

1+sinx

=  

1−sin  

2

x

1+sinx

 

=  

(1+sinx)(1−sinx)

1+sinx

=  

1−sinx

1

 

differentiate with respect to x

dx

d

(  

dx

dy

)=  

dx

d

(  

1−sinx

1

)

dx  

2

 

d  

2

y

=  

(1−sinx)  

2

 

(1−sinx)  

dx

d

(1)−(1)  

dx

d

(1−sinx)

 

=  

(1−sinx)  

2

 

cosx

 

Hence proved.

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