Question

prove tantheta + sectheta - 1/ tantheta - sectheta + 1 = 1+ sintheta/ costheta​

Answer 1

Answer:

proved

Step-by-step explanation:

Given  

prove tan theta + sec theta - 1/ tan theta - sec theta + 1 = 1+ sin theta/ cos theta  

ANSWER  

Now we have

Tan theta + sec theta – 1 / 1 + tan theta + sec theta

 Multiply both numerator and denominator by 1 + tan theta + sec theta  

 Now writing in the form a^2 – b^2 we get

 (Tan theta + sec theta)^2 – 1^2 / (1 + tan theta)^2 – sec^2 theta

 Tan^2 theta + sec^2 theta + 2 tan theta sec theta – 1 / 1 + 2 tan theta + tan^2 theta – sec^2 theta

  We know that 1 + tan^2 theta = sec^2 theta

So tan^2 theta + 1 + tan^2 theta + 2 tan theta sec theta– 1 / 2 tan theta

    We get tan theta + sec theta

               Sin theta / cos theta + 1 / cos theta

                 1 + sin theta / cos theta (proved)