How do you solve #\sec ^ { 2} \theta = 7+ \tan \theta#?

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Answer 1 · 2017-08-03T12:13:31

Solution : In # 0 <= theta <= 360 ; theta ~~ 71.57^0 , theta~~ 116.57^0, theta~~ 251.57^0 , theta~~296.57^0 #

# sec^2 theta = 7 +tan theta or 1 +tan^2 theta = 7 +tan theta # or

# tan^2 theta - tan theta -6 =0 # or

#tan^2 theta - 3tan theta +2tan theta -6 =0 # or

# tan theta (tan theta -3) + 2 ( tan theta-3) =0# or

#(tan theta -3)( tan theta +2) =0# So either

# tan theta= 3 or tan theta = -2# When

# tan theta= 3 :. theta = tan ^-1 3 ~~ 71.57^0 # or

# theta = 180+71.57^0 ~~ 251.57 ^0 # When

# tan theta= -2 :. theta = tan ^-1 (-2) ~~ -63.43^0 or 296.57^0# or

# theta = 180 - 63.43 ~~ 116.57^0 #

Solution : In # 0 <= theta <= 360 #

#theta ~~ 71.57^0 , 116.57^0, 251.57^0 , 296.57^0 # [Ans]