Find all exact angles x in the interval [0,360°] that satisfy the following equations (a)2tan²x +5tanx-3=0 (b)6cosx=secx +1 (c) 3cos x = cot x (d)csc x tan x = 5?

2 Answers
Nghi N.
Aug 28, 2015

Solve:
1. 2tan^2 x + 5tan x - 3 = 0.

Explanation:

Call tan x = t, we have to solve a quadratic equation:
#2t^2 + 5t - 3 = 0#
#D = d^2 = b^2 - 4ac = 25 + 24 = 49# --> #d = +- 7#
#t = -5/4 +- 7/4 = (-5 +- 7)/4#
#t = 1/2# and #t = -3#

a. #tan x = t = 1/2# --># x = 26.57# deg and #x = 206.57 #deg

b. #tan x = t = -3# --> #x = -71.57 (or 288.43)# and #x = 108.43# deg

Nghi N.
Aug 29, 2015

Solve : 6cos x = sec x + 1

Explanation:

#6cos x = 1/cos x + 1#
#6cos^2 x - cos x - 1 = 0# (Condition cos x not zero)
#D = d^2 = 1 + 24 = 25 #--> #d = +- 5#
#cos x = 1/12 +- 5/12#
a. #cos x = 6/12 = 1/2 #--> #x = +- 60 deg#
b.# cos x = -4/12 = -1/3 #--> #x = +- 109.47 # deg

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