Find the value of the expression

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

Correct option is B

Given:

The expression [cosec(75° + θ) – sec(15° – θ) – tan(55° + θ) + cot(35° – θ)]

Concept Used: 

cosec(90° - A) = sec A

sec(90° - A) = cosec A 

tan(90° - A) = cot A 

cot(90° - A) = tan A 

Solution:

sec(15° – θ) = cosec(90° - (15° – θ))

sec(15° – θ) = cosec(90° - 15° + θ)

sec(15° – θ) = cosec(75° + θ)

cot(35° – θ) = tan(90° - (35° – θ))

cot(35° – θ) = tan(90° - 35° + θ)

cot(35° – θ) = tan(55° + θ)

Now,

[cosec(75° + θ) – cosec(75° + θ) – tan(55° + θ) + tan(55° + θ)] = 0 – 0 = 0

Therefore, the value of the expression is 0.