If # tanA+secA=2 # then find #cosA #?

1 Answer
Steve M
Oct 27, 2016

#cosA=4/5 #

Explanation:

# tanA+secA=2 #

Substituting the definition of #tan# and #sec# gives us:
# sinA/cosA+1/cosA=2 #

Multiplying by #cosA#:
# sinA+1=2cosA #

# :. sinA=2cosA - 1#
# :. sin^2A=(2cosA - 1)^2#

Using the fundamental identity #sin^2X+cos^2X-=1#
# 1-cos^2A=(2cosA - 1)^2#
# :. 1-cos^2A=4cos^2A-4cosA+1#
# :. 5cos^2A-4cosA = 0#
# :. cosA(5cosA-4) = 0#
# cosA=0# or #5cosA-4 = 0 => cosA=4/5 #

We were told that A is an acute angle, so we can eliminate the solution # cosA=0#

Hence, #cosA=4/5 #

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