Question

The value of the expression [cosec (75° + θ) – sec (15° - θ) – tan

(55° + θ) + cot (35° - θ)] is

(A) 1

(B) −1

(C) 0

(D) 1/2​

please show the working

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

The value of the expression

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

(A) 1

(B) −1

(C) 0

(D) 1/2

FORMULA TO BE IMPLEMENTED

We are aware of Trigonometric formula that

1. cosec ( 90° - θ) = sec θ

2. tan ( 90° - θ) = cot θ

EVALUATION

Here the given expression is

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

= cosec [ 90° - (15° - θ)] - sec (15° - θ) - tan [ 90° - (35° - θ)] + cot (35° - θ)

= sec (15° - θ) - sec (15° - θ) - cot (35° - θ) + cot (35° - θ)

$= 0$

Hence the correct option is (C) 0

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