यदि ` theta ` ऐसा नयन कोण है कि ` tan theta + cot theta =2 `, तो ` tan^(7) theta + cot^(7) theta ` का मान ज्ञात करो ।

Explanation

दिया है :
` tan theta + cot theta =2 `
`implies tan theta +(1)/(tan theta )=2`
`(tan^(2) theta +1)/( tan theta )=2`
` implies tan^(2) theta - 2 tan theta +1=0`
`implies ( tan theta -1)^(2) =0`
` implies tan theta -1=0`
` implies tan theta =1 `
` implies tan theta =tan 45^(@) `
` implies theta =45^(@)`
`:. tan^(7) theta + cot^(7) theta = tan^(7) 45^(@) + cot^(7) 45^(@)=(tan 45^(@))^(7) + ( cot 45^(@))^(7) =(1)^(7) +(1)^(7)=2 `