Question

If sec theta + tan theta = m , show that m^2-1/m^2+1 = sin theta

Answer 1

Answer:solution:

Given,

sec + tan= m

» 1/cos + Sin/cos =m

( taking LCM then cross multiplication)

1 + sin = m. cos

(1 + sin )^2 =m^2 . cos^2

(Squaring both sides)

We know that sin square theta + cos square theta equal to 1 that implies cos square theta equal to 1 minus sin square theta

=> (1 + sin ) ^2 = m ^2(1 - sin^2)

We know that a square minus b square equal to a + b into a minus b

=> cancelling (sin + 1) both sides

=> 1 + sin = m ^2 (1-sin)

» 1 + sin=m^2 - m^2 -m^2.sin

Rearranging terms ,

we get,

sin + m^2.sin= m ^2 - 1

sin(1+m^2) =m^2 -1

=> sin = m^2 - 1 /m^2+1

Step-by-step explanation: