1.

यदि `2(cos^(2)theta-sin^(2)theta)=1` (`theta` एक धनात्मक न्यूनकोण है) तो `cottheta` किसके बराबर है?A. `-sqrt(3)`B. `(1)/(sqrt(3))`C. 1D. `sqrt(3)`

Answer» Correct Answer - d
`2 (cos^(2)theta-sin^(2)theta)=1`
`rArrcos^(2)theta-(1-cos^(2)theta)=(1)/(2)`
`rArrcos^(2) theta=(3)/(4)`
`rArrsec^(2)theta=(4)/(5)`
`rArr1+tan^(2)theta=(4)/(3)`
`rArrtan^(2)theta=(4)/(3)-1=(1)/(3)`
`rArr tantheta=(1)/sqrt(3)rArr cottheta=sq rt(3)`
Alternate
`2(cos^(2)theta-sin^(2)theta)=1`
`rArrcos^(2)theta-(1-cos^(2)theta)=(1)/(2)`
`rArr2cos^(2) theta=1+(1)/(2)rArr(3)/(2)`
`rArrcos^(2)theta=(3)/(4)`
`rArrcos theta=sqrt(3)/(2)`
`theta=30^(@)`
Hence,
`cot theta=cot30^(@)=sqrt(3)`


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