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The no. Of solutions of tan x + sec x = 2 cos x in [ 0 ,2π] is

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3 years ago

Arun
25768 Points
```							Dear student     tanx+sec x=2cosx => sin x/cos x + 1/cosx=2 cosx =>(sinx+1)/cosx = 2cosx => 1+sinx=2 cos^2 x=>1+sin x=2(1-sin^2 x) =>1+sinx -2(1+sinx)(1-sinx)=0 => (1+sinx)(1-2(1-sinx))=0 =>(1+sinx)(2sinx-1)=0so sin x=1, sin x=1/2so in between [0,2pi], the solutions are x=3pi/2, x=pi/6, x=5pi/6.therefore there are 3 solutions. RegardsArun(askIITians forum expert)
```
3 years ago
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• 31 Video Lectures
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• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions