Question

The value of the expression [cosec(75° + θ) – sec(15° – θ) – tan(55° + θ) + cot(35° – θ)] is ______.

Options

• – 1

• 0

• 1

• `3/2`

Answer 1

The value of the expression [cosec(75° + θ) – sec(15° – θ) – tan(55° + θ) + cot(35° – θ)] is 0.

Explanation:

According to the question,

We have to find the value of the equation,

cosec(75° + θ) – sec(15° – θ) – tan(55° + θ) + cot(35° – θ)

= cosec[90° – (15° – θ)] – sec(15° – θ) – tan(55° + θ) + cot[90° – (55° + θ)]

Since, cosec(90° – θ) = sec θ

And cot(90° – θ) = tan θ

We get,

= sec(15° – θ) – sec(15° – θ) – tan(55° + θ) + tan(55° + θ)

= 0