How do you simplify #f(theta)=csc2theta-sin2theta-5sec2theta# to trigonometric functions of a unit #theta#?

1 Answer
Dean R.
May 4, 2018

#f(theta) = 1/{2 sin theta cos theta} -2 sin theta cos theta - 5/{2 cos ^2 theta -1 }#

Explanation:

Here are the double angle formulas:

#cos(2 theta) = 2 cos^2 theta - 1 quad# among others

#sin(2 theta) = 2 sin theta cos theta #

# f(theta) = csc(2 theta) - sin(2 theta) - 5 sec(2 theta) #

#f(theta) = 1/sin(2 theta) - sin (2 theta) -5/cos(2theta)#

#f(theta) = 1/{2 sin theta cos theta} -2 sin theta cos theta - 5/{2 cos ^2 theta -1 }#

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