Answer the following questionIf - - is acute angle and tan- - cot - -2- find the values of tan7- - cot7-

tanθ>+cotθ>=2 as>AM>⩾>GM> or>(tanθ>+cotθ>/2)⩾>√(tanθ>+cotθ>) or>>tanθ>+cotθ>⩾>2> so&g ...

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Standard XII

Mathematics

Sum of Trigonometric Ratios in Terms of Their Product

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Answer the following question
If ' $θ$ ' is acute angle and $t a n θ + c o t θ - 2$ , find the values of $t a n^{7} θ + c o t^{7} θ = ?$

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Solution

$t a n θ + c o t θ = 2 a s A M ⩾ G M o r (\frac{t a n θ + c o t θ}{2}) ⩾ \sqrt{t a n θ + c o t θ} o r t a n θ + c o t θ ⩾ 2 s o t a n θ + c o t θ = 2 o n l y w h e n t a n θ = c o t θ = 1 ∴ θ = (\frac{π}{4}) ∴ t a n θ + c o t θ = 1^{7} + 1^{7} = 2$

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Answer the following questionIf 'θ' is acute angle and tanθ+cotθ−2, find the values of tan7θ+cot7θ=?

tanθ+cotθ=2asAM⩾GMor(tanθ+cotθ2)⩾√tanθ+cotθortanθ+cotθ⩾2sotanθ+cotθ=2onlywhentanθ=cotθ=1∴θ=(π4)∴tanθ+cotθ=17+17=2

Answer the following question
If ' $θ$ ' is acute angle and $t a n θ + c o t θ - 2$ , find the values of $t a n^{7} θ + c o t^{7} θ = ?$

$t a n θ + c o t θ = 2 a s A M ⩾ G M o r (\frac{t a n θ + c o t θ}{2}) ⩾ \sqrt{t a n θ + c o t θ} o r t a n θ + c o t θ ⩾ 2 s o t a n θ + c o t θ = 2 o n l y w h e n t a n θ = c o t θ = 1 ∴ θ = (\frac{π}{4}) ∴ t a n θ + c o t θ = 1^{7} + 1^{7} = 2$