evaluate cot 30/sec 30 + cosec 30//tan 45 - 2 cos 0//sin 30 + cos ^2 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
Cot30/sec30 + cosec 30 / tan45 -
2cos0 / sin30 + cos² 45
The question which you have posted cannot be solved using without using trigonometric tables. The answer is below
for formula refer attachment
= 3/2
