Question

Answer the following question? ​

Answer 1

Answer:

1/2

Step-by-step explanation:

we have to find value of cot30°/sec30° + cosec30°/tan45° - 2cos0°/sin30° + cos²45° without using trigonometric tables.

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

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