Simplify 1 + Cot² Using Trigonometric Identities: Learn How To Optimize Your Math Skills

1+cot^2

csc^2

We can simplify 1 + cot² using trigonometric identities.

Recall that cotangent is the reciprocal of tangent:

cot θ = 1/tan θ

Therefore, we can write:

1 + cot² θ = 1 + (1/tan² θ)

We can then use the Pythagorean identity to express tan² θ in terms of sin² θ and cos² θ:

tan² θ = sin² θ / cos² θ

Substituting this into the expression for 1 + cot² θ, we get:

1 + cot² θ = 1 + (1 / (sin² θ / cos² θ))

Simplifying this expression by taking the reciprocal of the fraction inside the parenthesis, we get:

1 + cot² θ = 1 + (cos² θ / sin² θ)

Now we can simplify further by adding the fractions:

1 + cot² θ = (sin² θ + cos² θ) / sin² θ

Using the Pythagorean identity again, we know that sin² θ + cos² θ = 1, so we can substitute:

1 + cot² θ = 1 / sin² θ

Finally, we can use the reciprocal identity for sine:

1 + cot² θ = csc² θ

Therefore, 1 + cot² θ simplifies to csc² θ.

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