MHT CET · Maths · Trigonometric Ratios & Identities
If \(\tan \theta+\cot \theta=4\), then \(\tan ^{4} \theta+\cot ^{4} \theta=\)
- A 194
- B 110
- C 80
- D 191
Answer & Solution
Correct Answer
(A) 194
Step-by-step Solution
Detailed explanation
\(\tan \theta+\cot \theta=4\)
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
\(\begin{array}{l}
\tan ^{4} \theta+\cot ^{4} \theta+2 \tan ^{2} \theta \cot ^{2} \theta=196 \\
\tan ^{4} \theta+\cot ^{4} \theta=196-2=194
\end{array}\)
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
\(\begin{array}{l}
\tan ^{4} \theta+\cot ^{4} \theta+2 \tan ^{2} \theta \cot ^{2} \theta=196 \\
\tan ^{4} \theta+\cot ^{4} \theta=196-2=194
\end{array}\)
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