If $\tan \theta+\cot \theta=4$, then $\tan ^{4} \theta+\cot ^{4} \theta=$

If $\tan \theta+\cot \theta=4$, then $\tan ^{4} \theta+\cot ^{4} \theta=$
  1. 194
  2. 110
  3. 80
  4. 191

Solution

$\tan \theta+\cot \theta=4$ On squaring both side, we get $\tan ^{2} \theta+\cot ^{2} \theta+2 \tan \theta \cot \theta=16 \Rightarrow \tan ^{2} \theta+\cot ^{2} \theta=14$ On squaring both side, we get $\begin{array}{l} \tan ^{4} \theta+\cot ^{4} \theta+2 \tan ^{2} \theta \cot ^{2} \theta=196 \\ \tan ^{4} \theta+\cot ^{4} \theta=196-2=194 \end{array}$

Asked in: MHT CET 2020 (20 Oct Shift 1)

Practice more Trigonometric Ratios & Identities questions on Aicharya