If tan (8θ – 11°) tan (11θ – 13°) = 1, then find the value of tan10θ + cot5θ

If tan (8θ – 11°) tan (11θ – 13°) = 1, then find the value of tan10θ + cot5θ

If tan (8θ – 11°) tan (11θ – 13°) = 1, then find the value of tan10θ + cot5θ ?

Sol:

We know, if tanA. tanB = 1

Then, A + B = 90°

Now,

Tan(8θ – 11) . tan (11θ – 13) = 1

∴ 8θ – 11 + 11θ – 13 = 90

⇒ 19θ = 114

⇒ θ = 6

Now,Tan10θ + cot 5θ

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