If tan #theta# + sec #theta#=2 then what is tan #theta# is equal to?

Question

If tan #theta# + sec #theta#=2 then what is tan #theta# is equal to?

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Answer 1 · 2017-08-17T11:43:38

Given #sectheta+tantheta=2....[1]#

we get

#sectheta-tantheta=(sec^2theta-tan^2theta)/(sectheta+tantheta)#

#sectheta-tantheta=1/2.....[2]#

Subtracting [2] from [1] we get

#2tantheta=2-1/2=3/2#

#=>tantheta=3/4=0.75#

Note:
#(sectheta-tantheta)(sectheta+tantheta)=sec^2theta-tan^2theta=1#

this comes from the formula

#sin^2theta+cos^2theta=1# dividing both sides by #cos^2theta#