Q96 / 180 · KCET 2020 · Mathematics

If $\tan A+\cot A=2$, then the value of $\tan ^{4} A+\cot ^{4} A=$

  • Correct answer
    A
    2
  • B
    1
  • C
    4
  • D
    5

Solution

We have, $\tan A+\cot A=2$ $\begin{aligned} &(\tan A+\cot A)^{2}=(2)^{2} \\ &\tan ^{2} A+\cot ^{2}+2=4 \\ &\tan ^{2} A+\cot ^{2} A=2 \\ &\left(\tan ^{2} A+\cot ^{2} A\right)^{2}=(2)^{2} \\ &\tan ^{4} A+\cot ^{4} A+2=4 \\ &\tan ^{4} A+\cot ^{4} A=2 \end{aligned}$

Hence, the correct answer is option: 'A'.

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