NIMCET 2020 Question Paper with solutions

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Question : 41 of 120

Marks: +1, -0

If

\cos x=\tan y, \cot y=\tan z

and

\cot z=\tan x

, then

\sin x=

:

${√5-1}/2$
${√5+1}/2$
${√5+1}/4$
${√5-1}/4$

Solution:

Given,

\cos x=\tan y

.....(1)

\tan y=\cot z

......(2)

\cot z=\tan x

....(3)
from equation (1),(2),(3)

\cos x=\tan x

\cos x=\sin x{/}\cos x

\cos^2x=\sin x

1-\sin^2x=\sin x

\sin^2x+\sin x-1=0

\sin x={-1±√{1+4}}/{2.1}

={-1±√5}/2

Since

-1 < \sin x < 1

\sin x={√5-1}/2

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