For the identity cos x + (cos x tan^2 x) = sec x
Show that it is true for x = 30 deg, using exact values
please help i am so stuck on this question
Thanks in advance
Show that it is true for x = 30 deg, using exact values
please help i am so stuck on this question
Thanks in advance
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30 degrees is one of the special angles you should have memorized for the purposes of this class. All you need to do is substitute x=30 into the entire equation, and verify that it is true. So then you must verify that
cos (30) + (cos (30) tan²(30) = sec (30). Start with the RHS
sec (30) = 1/cos (30). Using that cos (30) = 1/2, you get
sec (30) = 2
LHS
cos (30) + (cos (30)tan²(30)) =
(1/2) + ((1/2)(3)) (using that tan (30) = √3)
LHS = 1/2 + 3/2 = 4/2 = 2
Since LHS = RHS, this identity is true when x = 30.
cos (30) + (cos (30) tan²(30) = sec (30). Start with the RHS
sec (30) = 1/cos (30). Using that cos (30) = 1/2, you get
sec (30) = 2
LHS
cos (30) + (cos (30)tan²(30)) =
(1/2) + ((1/2)(3)) (using that tan (30) = √3)
LHS = 1/2 + 3/2 = 4/2 = 2
Since LHS = RHS, this identity is true when x = 30.