Question

without using trigonometric tables evaluate the following tan 30 degree divided by sec 30 degree + cosec 30 degree divided by tan 45 degree minus 2 cos 0 degree divided by sin 30 degree + cos square 45 degree ​

Answer 1

tan 30 degree divided by sec 30 degree + cosec 30 degree divided by tan 45 degree minus 2 cos 0 degree divided by sin 30 degree + cos square 45 degree ​

= tan 30°/sec 30° + cosec 30°/tan 45° - 2cos 0°/sin 30° + cos² 45

= (sin 30°/cos 30°) /sec 30° + cosec 30°/tan 45° - 2cos 0°/sin 30° + cos² 45

= sin 30° + cosec 30°/tan 45° - 2cos 0°/sin 30° + cos² 45

= 1/2 + 2/1 - 2 [ 1 / (1/2) ] + (1/√2)²

= 1/2 + 2 - 4 + 1/2

= 1 + 2 - 4

= 3 - 4

= -1