Question

Evaluate
8√3cosec²30° sin60° cos60° cos²45º sin45°tan30° cosec³ 45°​

Answer 1

Answer:

8√3cosec²30°.sin60°.cos60°.cos²45°.sin45°.tan30°.cosec²45°

= 8√3(2)².√3/2.1/2.(1/√2)².1/√2.1/√3.(√2)²

=4√2√3

=4√6

Answer 2

Answer:

=8√3cosec²30° sin60° cos60° cos²45º sin45°tan30° cosec³ 45°

=8√3×(2)²×√3/2×1/2×(1/√2)²×1/√2×√3×(√2)³

=

$= 8 \sqrt{3 } \times 2 {}^{2} \times \frac{ \sqrt{3}}{2} \times \frac{1}{2} \times ( \frac{1}{ \sqrt{2} } ) {}^{2} \times \frac{1}{ \sqrt{2} } \times \frac{1}{ \sqrt{3} } \times( \sqrt{2} ) {}^{3} \\ 32 \sqrt{3} \times \frac{ \sqrt{3} }{4} \times \frac{1}{2 \sqrt{2} } \times \frac{2 \sqrt{2} }{ \sqrt{3} } \\ = \frac{96}{4} \times \frac{1}{ \sqrt{3} } \\ = \frac{24}{ \sqrt{3} } \\ = 8 \sqrt{3}$