Sec #theta# -1#-:#sec #theta# =?

Question

I understand sign conversions, but I think it should be one, sine 1/cos and -1/1/cos would subtract to 1? but my options are 1+cos, -2tan^2 sec csc, sin tan. With thetas respectively.

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Answer 1 · 2018-02-15T07:43:04

#color(green)(1-cos theta)#

#sec theta = 1 / cos theta#

#(sec theta - 1 ) /sec theta = ((1/cos theta) - 1) / (1/cos theta)#

#=> (1 - cos theta) / cancel(cos theta) / (1/cancelcos theta) = 1-cos theta#