Math, asked by sumabr77311, 2 days ago

If theta in an acute angle and tan theta+cot theta=2.then find the value of tan^4theta+cot^4theta

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Answers

Answered by vipashyana1
1

Answer:

 tanθ + cotθ = 2 \\Squaring \: on \: both \: the \: sides \\  {(tanθ + cotθ)}^{2}  =  {(2)}^{2}  \\  {tan}^{2} θ +  {cot}^{2} θ + 2tanθcotθ = 4 \\  {tan}^{2} θ +  {cot}^{2} θ + 2 \times  \frac{sinθ}{cosθ}  \times  \frac{cosθ}{sinθ}  = 4 \\ {tan}^{2} θ +  {cot}^{2} θ + 2 = 4 \\  {tan}^{2} θ +  {cot}^{2} θ  = 4 - 2  \\  {tan}^{2} θ +  {cot}^{2}θ = 2 \\Squaring \: on \: both \: the \: sides \\  {( {tan}^{2} θ +  {cot}^{2}θ )}^{2}  =  {(2)}^{2}  \\  {tan}^{4} θ +  {cot}^{4} θ + 2 {tan}^{2}θ  {cot}^{2}θ  = 4 \\  {tan}^{4} θ +  {cot}^{4} θ + 2 \times  \frac{ {sin}^{2}θ }{ {cos}^{2}θ }  \times  \frac{ {cos}^{2}θ }{ {sin}^{2} θ}  = 4 \\ {tan}^{4} θ +  {cot}^{4} θ + 2 = 4 \\  {tan}^{4} θ +  {cot}^{4} θ  = 4 - 2 \\{tan}^{4} θ +  {cot}^{4} θ  =  2

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