How do you simplify the expression secthetatanthetacscthetasecθtanθcscθ?

2 Answers
Aug 9, 2016

=sec^2theta=sec2θ

Explanation:

secthetatanthetacscthetasecθtanθcscθ
=1/costheta times sintheta/costheta times 1/sintheta=1cosθ×sinθcosθ×1sinθ
=1/costheta times cancelsintheta/costheta times 1/cancelsintheta
=1/cos^2theta
=sec^2theta

Aug 9, 2016

sec^2(theta)

Explanation:

sec(theta)->1/cos(theta)

tan(theta)->(sin(theta))/(cos(theta))

csc(theta)->1/(sin(theta))
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Putting this all together gives:

1/cos(theta)xx(cancel(sin(theta)))/cos(theta) xx1/(cancel(sin(theta))

=1/cos^2(theta) = sec^2(theta)