How do you prove #\tan ( \frac { 3\pi } { 4} - \theta ) = \frac { - 1- \tan \theta } { 1- \tan \theta }#?

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Answer 1 · 2017-04-23T16:30:11

Please see below.

#tan((3pi)/4-theta)#

= #tan(pi-pi/4-theta)#

= #tan(pi-(pi/4+theta))#

= #-tan(pi/4+theta)#

= #-(tan(pi/4)+tantheta)/(1-tan(pi/4)tantheta)#

= #-(1+tantheta)/(1-1xxtantheta)#

= #(-1-tantheta)/(1-tantheta)#