How do you simplify $(1 + sec theta)/sec theta = sin^2 theta/(1 - cos theta)$ ?

Question

21859 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-11-27T21:21:12

Please look at the explanation

Remember: The trigonometric identities '

$sin^2theta+cos^2theta= 1$ $hArr$ $sin^2theta= 1-cos^2theta$

$1/costheta= sectheta$ $hArr$ $1/sectheta= costheta$

$(1+sectheta)/sectheta = (sin^2theta)/(1-costheta)$

$=>$ If we start from the right hand side, multiply by the conjugate of the denominator

$(1+sectheta)/sectheta = [(sin^2theta)/(1-costheta)]color(red)([(1+costheta)/(1+costheta)]$

$(1+sectheta)/sectheta = ((sin^2theta)(1+costheta)]/(1-cos^2theta)$

$(1+sectheta)/sectheta = [(sin^2theta)(1+costheta)]/(sin^2theta)$

$(1+sectheta)/sectheta = [cancel(sin^2theta) (1+costheta)]/(cancel(sin^2theta)$

$(1+sectheta)/sectheta = 1+costheta$

$(1+sectheta)/sectheta = 1+1/(sectheta)$ common denominator

$(1+sectheta)/sectheta = 1*[color(red)sectheta]/color(red)sectheta+1/(sectheta)$

$(1+sectheta)/sectheta = (1+sectheta)/sectheta$

Done!

How do you simplify (1 + sec theta)/sec theta = sin^2 theta/(1 - cos theta)(1 + sec theta)/sec theta = sin^2 theta/(1 - cos theta)?