Grade 11Trigonometry
Number of solutions of tanx +secx=2cosx lying in 0,2×180 is
1 Answer
Arun
tan x + sec x = 2cos x
So , (1+sin x) / cos x = 2cos x
==> 1 + sin x = 2 cos^2 x
==> 1 + sin x = 2(1-sin^2 x)
==> 2sin^2 x + sin x -1 = 0
==> sin x = -1 or sin x = 1/2
So there are a total of 3 solutions I think.
Note: sin x = 1/2 has 2 solutions , 30 and 150 (in degrees) and sin x = -1 has one solution.
So , (1+sin x) / cos x = 2cos x
==> 1 + sin x = 2 cos^2 x
==> 1 + sin x = 2(1-sin^2 x)
==> 2sin^2 x + sin x -1 = 0
==> sin x = -1 or sin x = 1/2
So there are a total of 3 solutions I think.
Note: sin x = 1/2 has 2 solutions , 30 and 150 (in degrees) and sin x = -1 has one solution.
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