Question

Cosec (180" -
2 sin e. sec (90° + 0). sin 30°.tan 135º = 1​

Answer 1

Step-by-step explanation:

Explanation:

Given below is the list containing all 6 trigonometric ratios for the above mentioned angles.

1) 120º

sin 120° = sin (1 × 90° + 30°) = cos 30° = √3/2

cos 120° = cos (1 × 90° + 30°) = – sin 30° = – 1/2

tan 120° = tan (1 × 90° + 30°) = – cot 30° = – √3

csc 120° = csc (1 × 90° + 30°) = sec 30° = 2/√3

sec 120° = sec (1 × 90° + 30°) = – csc 30° = – 2

cot 120° = cot (1 × 90° + 30°) = – tan 30° = – 1/√3

2) -135º

sin (- 135°)= – sin 135°= – sin (1 × 90°+ 45°) = – cos 45° = – 1√2

cos (- 135°)= cos 135°= cos (1 × 90°+ 45°) = – sin 45°= – 1√2

tan (- 135°) = – tan 135° = – tan ( 1 × 90° + 45°) = – (- cot 45°) = 1

csc (- 135°)= – csc 135°= – csc (1 × 90°+ 45°)= – sec 45° = – √2

sec (- 135°)= sec 135°= sec (1 × 90°+ 45°)= – csc 45°= – √2

cot (- 135°) = – cot 135° = – cot ( 1 × 90° + 45°) = – (-tan 45°) = 1

3) 150º

sin 150° = sin (2 × 90° – 30°) = sin 30° = 1/2

cos 150° = cos (2 × 90° – 30°) = - cos 30° = – √3/2

tan 150° tan (2 × 90° – 30°) = - tan 30° = – 1√3

csc 150° = csc (2 × 90° – 30°) = csc 30° = 2

sec 150° = sec (2 × 90° – 30°) = sec 30° = – 2√3

cot 150° = cot (2 × 90° – 30°) = – cot 300 = – √3

4) 180º

sin 180° = sin (2 × 90° – 0°) = sin 0° = 0

cos 180° = cos (2 × 90° – 0°) = – cos 0° = – 1

tan 180° = tan (2 × 90° + 0°) = tan 0° = 0

csc 180° = csc (2 × 90° – 0°) = csc 0° = Undefined

sec 180° = sec (2 × 90° – 0°) = – sec 0° = – 1

cot 180° = cot (2 × 90° + 0°) = cot 0° = Undefined

5) 270º

sin 270° = sin (3 × 90° + 0°) = – cos 0° = – 1

cos 270° = cos (3 × 90° + 0°) = sin 0° = 0

tan 270° = tan (3 × 90° + 0°) = – cot 0° = Undefined

csc 270° = csc (3 × 90° + 0°) = – sec 0° = – 1

sec 270° = sec (3 × 90° + 0°) = csc 0° = Undefined

cot 270° = cot (3 × 90° + 0°) = – tan 0° = 0

Thus, we have calculated the given angle values for all the trigonometric ratios.