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  1. If tanθ + cotθ = 5, then the value of tan2θ + cot2θ is
    1. 22
    2. 25
    3. 23
    4. 27
Correct Option: C

tanθ + cotθ = 5
On squaring both sides,
(tanθ + cotθ)2 = 25
⇒  tan2θ + cot2θ + 2tanθ. cotθ = 25
⇒  tan2θ + cot2θ + 2 = 25
⇒  tan2θ + cot2θ = 25 – 2 = 23


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