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Mathematics · 2025 · 2 marks
CBSE 2025 · Region 3 · Set 3 · Q21
If tan A + cot A =6, then find the value of tan^2 A + cot^2 A -4.
If $\displaystyle \tan \mathrm{A}+\cot \mathrm{A}=6$, then find the value of $\displaystyle \tan ^{2} \mathrm{~A}+\cot ^{2} \mathrm{~A}-4$.
Marking-scheme solution
\(\displaystyle (\tan \mathrm{A}+\cot \mathrm{A})^{2}=36\)
\(\displaystyle \tan ^{2} \mathrm{~A}+\cot ^{2} \mathrm{~A}+2 \tan \mathrm{~A} \cot \mathrm{~A}=36\)
\(\displaystyle \tan ^{2} \mathrm{~A}+\cot ^{2} \mathrm{~A}=34\)
\(\displaystyle \therefore \tan ^{2} \mathrm{~A}+\cot ^{2} \mathrm{~A}-4=30\)
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CBSE Class 10 Mathematics past-paper question from the 2025 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.