Without using trigonometric tables evaluate- cot 30/sec30+cosec30/tan45 - 2cos0/sin30 +cos power2 45
Answers
value of given expression is 1/2
we have to find value of cot30°/sec30° + cosec30°/tan45° - 2cos0°/sin30° + cos²45° without using trigonometric tables.
let's solve it !
cot30°/sec30° + cosec30°/tan45° - 2cos0°/sin30° + cos²45°
= cos30°. sec30°/sin30° + cosec30°/tan45° - 2cos0°. cosec30° + cos²45°
= cosec30° + cosec30°.cot45° - 2cos0°.cosec30° + cos²45°
= cosec30°(1 + cot45° - 2cos0°) + cos²45
= cosec30°(tan45° + cot45° - 2cos0°) + cos²45°
= cosec30°( sin45°/cos45° + cos45°/sin45° - 2cos0°) + cos²45°
= cosec30°{(sin²45° + cos45°)/sin45°.cos45° - 2cos0°} + cos²45°
= cosec30°{1/(1/2)(2sin45°.cos45°) - 2cos0°} + cos²45°
= cosec0° {2/sin90° - 2cos0°} + cos²45
= cosec0° {2/1 - 2 × 1 } + (1/√2)²
= 0 + 1/2
= 1/2
Answer:
value of given expression is 1/2
we have to find value of cot30°/sec30° + cosec30°/tan45° - 2cos0°/sin30° + cos²45° without using trigonometric tables.
let's solve it !
cot30°/sec30° + cosec30°/tan45° - 2cos0°/sin30° + cos²45°
= cos30°. sec30°/sin30° + cosec30°/tan45° - 2cos0°. cosec30° + cos²45°
= cosec30° + cosec30°.cot45° - 2cos0°.cosec30° + cos²45°
= cosec30°(1 + cot45° - 2cos0°) + cos²45
= cosec30°(tan45° + cot45° - 2cos0°) + cos²45°
= cosec30°( sin45°/cos45° + cos45°/sin45° - 2cos0°) + cos²45°
= cosec30°{(sin²45° + cos45°)/sin45°.cos45° - 2cos0°} + cos²45°
= cosec30°{1/(1/2)(2sin45°.cos45°) - 2cos0°} + cos²45°
= cosec0° {2/sin90° - 2cos0°} + cos²45
= cosec0° {2/1 - 2 × 1 } + (1/√2)²
= 0 + 1/2
= 1/2