Question

What will be the value of tan\:\theta-cot\:\thetatanθ−cotθ in an isosceles right triangle?

Answer 1

Answer:

your answer is -1

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Answer 2

Value of tan θ - (cot θ * tan θ) − cot θ in an isosceles right triangle.

Given,

An isosceles right triangle

To find,

tan θ - (cot θ * tan θ) − cot θ

Solution,

Given is an isosceles right triangle.

One angle of the triangle would then be 90°. The sum of the other two angles would be (180-90) = 90°.

Since it is an isosceles triangle, both other angles are equal.

Which implies 2θ = 90°

or, θ = 45°

Now, replacing θ = 45° in tan θ - (cot θ * tan θ) − cot θ,

tan 45° - (cot 45° * tan 45°) - cot 45°

tan 45° = 1 and cot 45° = 1

or, 1 - (1*1) - 1 = 1 - 2 = -1

tan θ - (cot θ * tan θ) − cot θ = -1

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