Question

​if sec a is equals to m square + 1 divided by 2 m find tan a and sin a​

Answer 1

Answer:

Step-by-step explanation:

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

Thank you

Answer 2

Answer:

sec a= hyp/ base= (m²+1)/2m

So perpendicular=√[ (m²+1)²-4m²]

= √[m⁴+1-2m²]= √(m²-1)² = m²-1

Therefore

tan a= perpendicular/ base

= (m²-1)/2m. and

sin a= perpendicular/ hyp= (m²-1)/(m²+1)