If tantheta = x - 1/4x   find sectheta - tan <br />
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theta in terms of x

Asked by ahuja8087 | 12th Sep, 2015, 01:28: PM

Expert Answer:

G i v e n space t h a t space tan theta equals x minus fraction numerator 1 over denominator 4 x end fraction... left parenthesis 1 right parenthesis W e space k n o w space t h a t comma space s e c squared theta minus tan squared theta equals 1 rightwards double arrow space s e c squared theta equals 1 plus t a n squared theta rightwards double arrow space s e c squared theta equals 1 plus open parentheses x minus fraction numerator 1 over denominator 4 x end fraction close parentheses squared rightwards double arrow space s e c squared theta equals 1 plus x squared plus fraction numerator 1 over denominator 16 x squared end fraction minus 2 cross times x cross times fraction numerator 1 over denominator 4 x end fraction rightwards double arrow space s e c squared theta equals 1 plus x squared plus fraction numerator 1 over denominator 16 x squared end fraction minus 1 half rightwards double arrow space s e c squared theta equals x squared plus fraction numerator 1 over denominator 16 x squared end fraction plus 1 half rightwards double arrow space s e c squared theta equals x squared plus fraction numerator 1 over denominator 16 x squared end fraction plus 2 cross times x cross times fraction numerator 1 over denominator 4 x end fraction rightwards double arrow space s e c squared theta equals open parentheses x plus fraction numerator 1 over denominator 4 x end fraction close parentheses squared rightwards double arrow s e c theta equals x plus fraction numerator 1 over denominator 4 x end fraction... left parenthesis 2 right parenthesis C o n s i d e r space e q u a t i o n s space left parenthesis 1 right parenthesis space a n d space left parenthesis 2 right parenthesis T h u s comma space s e c theta minus tan theta equals x plus fraction numerator 1 over denominator 4 x end fraction minus open parentheses x minus fraction numerator 1 over denominator 4 x end fraction close parentheses space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals x plus fraction numerator 1 over denominator 4 x end fraction minus x plus fraction numerator 1 over denominator 4 x end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 2 over denominator 4 x end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 1 over denominator 2 x end fraction

Answered by Vimala Ramamurthy | 12th Sep, 2015, 05:45: PM