If tan theta + cot theta = 2, prove tan^2 theta + cot^2 theta = 2
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Answer: We have, tanθ+cotθ=2
⇒(tanθ+cotθ)2=(2)2
⇒tan2θ+cot2θ+2tanθ+2tanθcotθ=4
⇒tan2θ+cot2θ+2=4
⇒tan2θ+cot2θ=2
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