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Number of solutions of tanx +secx=2cosx lying in 0,2×180 is

Number of solutions of tanx +secx=2cosx lying in 0,2×180 is

Grade:11

1 Answers

Arun
25757 Points
5 years ago
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.

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