Question

The value of sin 135° cosec 225° tan 150° cot 315° is ______.

Options

• `-1/sqrt(5)`

• `-1/sqrt(3)`

• `1/sqrt(2)`

• 1

Answer 1

The value of sin 135° cosec 225° tan 150° cot 315° is `underlinebb(-1/sqrt(3))`.

Explanation:

sin 135° cosec 225° tan 150° cot 315°

= sin(180° – 45°) cosec(180° + 45°) tan(180° – 30°) cot(360° – 45°)

= sin 45° (– cosec 45°) (– tan 30°) (– cot 45°)

`[((∵ sin(180^circ - θ) = sin θ",", "cosec" (180^circ + θ) = -  "cosec"  θ)),(tan(180^circ - θ) = - tan θ and cot(360^circ - θ) = - cot θ)]`

= – sin 45° cosec 45° tan 30° cot 45°

= `-1/sqrt(2) . sqrt(2) . 1/sqrt(3) . 1`

= `-1/sqrt(3)`