Question

[ cos² θ + tan θ csc θ = cos θ ]

a) True
b) False

Answer 1

The equation cos² θ + tan θ csc θ = cos θ is false.

Step-by-step explanation:

The given expression is cos² θ + tan θ csc θ = cos θ. To determine if this equation is true or false, we can simplify it using trigonometric identities. First, we know that csc θ is the reciprocal of sine, so we can replace it with 1/sin θ. Next, we can use the identity tan θ = sin θ / cos θ. Substituting these values into the equation, we have cos² θ + (sin θ / cos θ) (1/sin θ) = cos θ.

Simplifying further, we have cos² θ + 1/cos θ = cos θ.

Combining fractions, we have (cos² θ * cos θ + 1) / cos θ = cos θ.

Now, multiplying through by cos θ, we have cos³ θ + 1 = cos² θ.

Since this equation is not true for all values of θ, the original statement b) False is correct.