KCET · Maths · Binomial Theorem
If \(\tan A+\cot A=2\), then the value of \(\tan ^{4} A+\cot ^{4} A=\)
- A 2
- B 1
- C 4
- D 5
Answer & Solution
Correct Answer
(A) 2
Step-by-step Solution
Detailed explanation
We have, \(\tan A+\cot A=2\)
\(\begin{aligned}
&(\tan A+\cot A)^{2}=(2)^{2} \\
&\tan ^{2} A+\cot ^{2}+2=4 \\
&\tan ^{2} A+\cot ^{2} A=2 \\
&\left(\tan ^{2} A+\cot ^{2} A\right)^{2}=(2)^{2} \\
&\tan ^{4} A+\cot ^{4} A+2=4 \\
&\tan ^{4} A+\cot ^{4} A=2
\end{aligned}\)
\(\begin{aligned}
&(\tan A+\cot A)^{2}=(2)^{2} \\
&\tan ^{2} A+\cot ^{2}+2=4 \\
&\tan ^{2} A+\cot ^{2} A=2 \\
&\left(\tan ^{2} A+\cot ^{2} A\right)^{2}=(2)^{2} \\
&\tan ^{4} A+\cot ^{4} A+2=4 \\
&\tan ^{4} A+\cot ^{4} A=2
\end{aligned}\)
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