If tan theta-cot theta= 3, then prove that tan² theta + cot² theta= 11
Answers
Step-by-step explanation:
tanA - cotA = 3
Squaring on both sides
(tanA - cotA)² = (3)²
tan²A + cot²A - 2(tanA)(cotA) = 9
tan²A + cot²A - 2(tanA)(1/tanA) = 9
tan²A + cot²A - 2 = 9
tan²A + cot²A = 9 + 2
tan²A + cot²A = 11.
Answer:
Answer:
\begin{gathered}Value \: of \\ tan^{2}\theta+cot^{2}\theta = 2\end{gathered}
Valueof
tan
2
θ+cot
2
θ=2
Step-by-step explanation:
Given \: tan\theta+cot\theta=2\:---(1)Giventanθ+cotθ=2−−−(1)
/* On Squaring both sides of the equation, we get
\left(tan\theta+cot\theta\right)^{2}=2^{2}(tanθ+cotθ)
2
=2
2
\implies tan^{2}\theta+cot^{2}\theta+2 tan\theta cot\theta = 4⟹tan
2
θ+cot
2
θ+2tanθcotθ=4
\implies tan^{2}\theta+cot^{2}\theta+2 \times 1 = 4⟹tan
2
θ+cot
2
θ+2×1=4
/* tanAcotA = 1 */
\implies tan^{2}\theta+cot^{2}\theta = 4-2⟹tan
2
θ+cot
2
θ=4−2
\implies tan^{2}\theta+cot^{2}\theta = 2⟹tan
2
θ+cot
2
θ=2
Therefore,
tan^{2}\theta+cot^{2}\theta = 2tan
2
θ+cot
2
θ=2
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