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Question

Find x from the following equations:

(i)cosec(90+θ)+xcosθcot(90+θ)

=sin(90+θ)

(ii)xcot(90+θ)+tan(90+θ)sinθ+cosec(90+θ)=0


Solution

(i)cosec(90+θ)+xcosθcot(90+θ)

=sin(90+θ)

secθ+xcosθx(tanθ)=cosθ

1cosθ+xcosθx(sinθ)cosθ=cosθ

1cosθxsinθ=cosθ

1xsinθcosθcosθ=cosθ

1xsinθcosθ=cos2θ

1cos2θ=xsinθcosθ

sin2θ=xsinθcosθ

sinθ=xcosθ

x=sinθcosθ

=tanθ

Hence x=tanθ

(ii)We have xcot(90+θ)+tan(90+θ)sinθ+cosec(90+θ)=0

x(tanθ)cotθ×sinθ+secθ=0

xtanθcosθsinθ×sinθ+1cosθ=0

xsinθcosθcosθ+1cosθ=0

xsinθcos2θ+1cosθ=0

xsinθ+1cos2θ=0

xsinθ+sin2θ=0

xsinθ=sin2θ

x=sin2θsinθ

x=sinθ


Mathematics
RD Sharma
Standard XI

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