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Question

If (tan θ + cot θ) = 5 then (tan2 θ + cot2 θ) = ?

(a) 27 (b) 25 (c) 24 (d) 23

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Solution

(tan θ + cot θ) = 5 (given)

(tanθ+cotθ)2=(5)2(squaring both sides)

tan2θ+cot2θ+2×tanθ×cotθ=25

[(a+b)2=a2+b2+2ab]

tan2θ+cot2θ+2×1=25

tanθ×cotθ=tanθ×1tanθ=1)

tan2θ+cot2θ=252=23


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