Question

If tan theta + cot theta = 5 , then find tan square theta + cot square theta

Answer 1

Answer:

This is a very simple question of trigonometry.  Let theta = ∅

Step-by-step explanation:

It is given that tan∅ + cot∅ = 5

On squaring the above equation, we get tan²∅ + cot²∅ + 2 tan∅.cot∅ = 5²

tan²∅ + cot²∅ + 2 = 25 ( tan∅.cot∅ = tan∅.(1/tan∅) = 1)

Therefore, tan²∅ + cot²∅ = 23.

Hence, the value of tan²∅ + cot ²∅ = 23

Answer 2

Concept Introduction:

The ratio of the length of the opposite side to the length of the adjacent side is equal to the Tan theta of right angled triangle.

Given:

We have been given, tanθ+cotθ=5

To Find:

tan ^2 θ+cot^2 θ

Solution:

Given,

tanθ+cotθ=5

Now squaring both sides we get,

or, (tan^2 θ+cot^2θ+2.tanθ.cotθ)=25

or, tan^2 θ+cot^2 θ=25−2 [ Since tanθ.cotθ=1]

or, tan^2 θ+cot^2 θ=23.

Final Answer:

tan^2 θ+cot^2 θ=23

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