How do you express #cos theta - cos^2 theta + sec theta # in terms of #sin theta #?

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Answer 1 · 2016-03-10T04:09:18

#sqrt(1-sin^2 theta)-(1-sin^2 theta)+1/sqrt(1-sin^2 theta)#
just simplify it further if you need to.

From the given data:
How do you express #cos theta−cos^2 theta+sec theta# in terms of
#sin theta#?

Solution:

from the fundamental trigonometric identities

#Sin^2 theta+Cos^2 theta=1#
it follows

#cos theta=sqrt(1-sin^2 theta)#

#cos^2 theta=1-sin^2 theta#

also

#sec theta=1/cos theta#

therefore

#cos theta−cos^2 theta+sec theta#

#sqrt(1-sin^2 theta)-(1-sin^2 theta)+1/sqrt(1-sin^2 theta)#

God bless...I hope the explanation is useful.