Question

prove that tanθ/secθ+1=secθ−1​/tanθ​

Answer 1

Answer:LHS =  

tanθ−secθ−1

tanθ+secθ−1

​

 

       =  

tanθ−secθ

tanθ+secθ−sec  

2

θ+tan  

2

θ

​

 

       =  

(tanθ−secθ)

(tanθ+secθ)−(secθ+tanθ)(secθ−tanθ)

​

 

       =  

(tanθ−secθ+1)

(tanθ+secθ)(1−secθ+tanθ)

​

 

       =tanθ+secθ (RHS)

                                    (proved)

Step-by-step explanation: pls mark 5 star

Answer 2

Consider the LHS.

⇒  

tanθ−secθ+1

tanθ+secθ−1

​

 

⇒  

tanθ−secθ+1

tanθ+secθ−(sec  

2

θ−tan  

2

θ)

​

 

(∵sec  

2

θ−tan  

2

θ=1)

⇒  

tanθ−secθ+1

(tanθ+secθ)−(secθ+tanθ)(secθ−tanθ)

​

 

(∵a  

2

−b  

2

=(a+b)(a−b))

⇒  

tanθ−secθ+1

(tanθ+secθ)[1−(secθ−tanθ)]

​

 

⇒  

tanθ−secθ+1

(tanθ+secθ)(tanθ−secθ+1)

​

 

⇒tanθ+secθ=  

cosθ

sinθ

​

+  

cosθ

1

​

=  

cosθ

1+sinθ

​

 

Here,

LHS=RHS

Hence proved.

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