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

See All answers

  1. Good web site you have got here.. It’s hard to find high quality writing like yours nowadays. I seriously appreciate individuals like you! Take care!!

My Thought

Your email address will not be published. Required fields are marked *

Our Tool : hike percentage calculator