Question

sec theta +tan theta = P prove that p^2-1/p^2+1=sin theta

Answer 1

hope this will help you

Answer 2

Hey there !!

From LHS -

p² -1 / p² + 1 = ( secⲫ + tanⲫ ) - 1 / ( secⲫ + tanⲫ)² + 1

=> sec²Ⲫ + tan² + 2secⲪtanⲪ - 1 / sec²Ⲫ + tan² + 2secⲪtanⲪ + 1

=> ( sec². ⲫ - 1) + tan ² + 2sec ⲫtanⲫ / secⲫ ² + 2 secⲫ tanⲫ + ( 1 + tanⲫ. ²)

=> tan² ⲫ + tan² ⲫ + 2sec. ⲫ tan ⲫ/ sec.²ⲫ + 2 secⲫ tanⲫ + sec.² ⲫ

=> 2tan. ² ∅ + 2tan∅sec∅ / 2 sec∅²+ 2sec∅ tan∅

=> 2tan∅ ( tan∅ + sec∅) / 2 sec∅( sec∅+ tan∅)

=> tan∅/ sec∅

=> sin∅ / cos∅ . sec∅

=> sin∅ ➣ RHS


Proved

Hope this would help you !!