Question

If tanθ + cot θ = 5, θ find tan 2 θ + cot 2 θ
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Answer 1

Question

If tanθ + cot θ = 5, θ find tan²θ + cot²θ

Solution

Given,

tanθ+cotθ=5

Now squaring both sides we get,

(tanθ+cotθ)²=5²

by using identity${\boxed{\sf{\red{(a+b)²=a²+b²+2ab}}}}$

⇒(tan²θ+cot²θ+2×tanθ×cotθ)=25

⇒(tan²θ+cot²θ+2×1)=25

⇒(tan²θ+cot²θ)=25

⇒tan²θ+cot²θ=25−2 [Since tanθ×cotθ=1]

⇒tan²θ+cot²θ=23

hope it helps ☺️

Answer 2

tanθ+cotθ=5

Now squaring both sides we get,

(tanθ+cotθ)²=5²

by using identity

(a+b)²=a²+b²+2ab

⇒(tan²θ+cot²θ+2×tanθ×cotθ)=25

⇒(tan²θ+cot²θ+2×1)=25

⇒(tan²θ+cot²θ)=25

⇒tan²θ+cot²θ=25−2 [Since tanθ×cotθ=1]

⇒tan²θ+cot²θ=23

hope it helps ☺️