## Prove that tanq+Secq-1÷tanq-secq+1=cosq÷1-sinq

Here am going to explain the steps Prove that tanq+Secq-1÷tanq-secq+1=cosq÷1-sinq

LHS => tanq+Secq-1/tanq-secq+1

=> (sinQ/cosQ+1/cosQ-1)/(sinQ/cosQ-1/cosQ+1) (divide nominator and denominate by cosQ)

=> (sinQ+1-cosQ)/(sinQ-1+cosQ) (Multipy nominator and denominate by (1-sinQ))

=> (1-sinQ)(sinQ+1-cosQ)/(1-sinQ)(sinQ-1+cosQ)

=> (sinQ+1-cosQ-sinQ2-sinQ+sinQ*cosQ)/(1-sinQ)(sinQ-1+cosQ)

=> (1-cosQ-sinQ2+sinQ*cosQ)/(1-sinQ)(sinQ-1+cosQ)
=> (1-sinQ2-cosQ+sinQ*cosQ)/(1-sinQ)(sinQ-1+cosQ)

=> (cosQ2-cosQ+sinQ*cosQ)/(1-sinQ)(sinQ-1+cosQ)
=> cosQ(cosQ-1+sinQ)/(1-sinQ)(sinQ-1+cosQ)

=> cosQ(cosQ-1+sinQ)/(1-sinQ)(cosQ-1+sinQ)
=> cosQ/(1-sinQ) = RHS

Hence proved

## working model in mathematics ?

Here am going to help you to create working model in mathematics

we have famous mathematical theorem

The volume of a cone is  one-third of volume of cube having same radius and height.By using this theorem we are going to make working model in mathematics

we know volume of cube having height h and radius r is πr2h

also volume of cone having height h and radius r  is    1/3πr2h

Here is details explanation of working model in mathematics

This is the video tutorial of working model in mathematics

## prove that sinQ-cosQ+1/sinQ+cosQ-1 =1/secQ-tanQ

To prove that sinQ-cosQ+1/sinQ+cosQ-1 =1/secQ-tanQ

Consider LHS

LHS => SinQ-cosQ+1/sinQ+cosQ+1

=>  (sinQ/cosQ-cosQ/cosQ+1/cosQ)/(sinQ/cosQ+cosQ/cosQ-1/cosQ)                   (divide nominator and denominate by cosQ)

=>  (tanQ-1+secQ)/(tanQ+1-secQ)

=> (tanQ+secQ-1)/(tanQ-secQ+1)

=> (tanQ+secQ-1)/(tanQ-secQ+(sec²Q-tan²Q)     (since sec²Q-tan²Q=1)

=> (tanQ+secQ-1)/(tanQ-secQ+[(secQ-tanQ)(secQ+tanQ)]

=> (tanQ+secQ-1)/-(secQ-tanQ)+[(secQ-tanQ)(secQ+tanQ)]

=>(tanQ+secQ-1)/(secQ-tanQ)[(secQ+tanQ)-1]

=> 1/secQ-tanQ  (since  (tanQ+secQ-1)/[(secQ+tanQ)-1]=1)

=> RHS

=> Hence Proved