Grade 11Trigonometry

if a=sec theta - tan theta, b=cosec theta + cot theta; calculate a in terms of b

A G M

9 Years agoGrade 11

3 Answers

Sayam

9 Years ago

b=cosec $\Theta$ +cot $\Theta$ =(1+cos $\Theta$ ) / sin $\Theta$ = cot $\Theta$ /2

a=sec $\Theta$ -tan $\Theta$ =(1-sin $\Theta$ )/cos $\Theta$

=1-cos( $\pi$ /2- $\Theta$ )/sin( $\pi$ /2- $\Theta$ )
=2sin²( $\pi$ /4- $\Theta$ /2) / 2sin( $\pi$ /4- $\Theta$ /2) cos( $\pi$ /4- $\Theta$ /2)
=tan( $\pi$ /4- $\Theta$ /2)=(1-tan $\Theta$ /2) / (1+tan $\Theta$ /2)

=(1-1/b) / (1+1/b)

=b-1/b+1...... ans

hope this clears your doubt

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6 Years ago

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