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.

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

 

 

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