tan theta + cot theta = 2 then find tan²theta + cot²theta = ?
Answers
Answer:
Let Tan theta be x
As Cot = 1/tan
1/tan = 1/x
x + 1/x = 2
(x+1/x) ^2 = x^2 + 1/x^2 + 2
(2) ^2 = x^2 + 1/x^2 + 2
4-2 = x^2 + 1/x^2
2 = x^2+ + 1/x^2
Therefore,
Tan^2 theta + Cot^2 theta = 2
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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