Question

Solve these? and explain​

Answer 1

Step-by-step explanation:

1)

sin30•sin60•sin90

1/2•√3/2•1

√3/4•1

√3/4

2)

2+√3•√3•1•1/√3•1/2+√3

(2√3+3)•(1/2√3+3)

=1

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Answer 2

$1)\frac{1}{2\sqrt{2}} \: or \: {2}^{ - \frac{3}{2} }$

$2)1$

Step-by-step explanation:

$1) \sin3x \times \sin6x \times \sin9x$

$\: \: \: \: \: when \: x = 10\degree,$

$\: \: \: \: \: \sin30\degree \times \sin60\degree \times \sin90\degree$

$\: \: \: \: \: \frac{1}{2} × \frac{1}{ \sqrt{2} } × 1$

$\: \: \: \: \: \frac{1}{2 \sqrt{2} }$

$2) \cot15\degree × \cot30\degree × \cot45\degree × \cot60\degree × \cot75\degree$

$\: \: \: \: \: \cot(45\degree - 30\degree) \times \sqrt{3} \times 1 \times \frac{1}{ \sqrt{3}} \times \cot(45\degree + 30\degree)$

$\: \: \: \: \: \frac{ \cot(45\degree) \cot(30\degree) + 1}{ \cot(30\degree) - \cot(45\degree) } \times \frac{ \cot(45\degree) \cot(30\degree) - 1}{ \cot(30\degree) + \cot(45\degree) }$

$\: \: \: \: \: \frac{1 \times \sqrt{3} + 1}{ \sqrt{3} - 1} \times \frac{1 \times \sqrt{3} - 1}{ \sqrt{3} + 1}$

$\: \: \: \: \: \frac{3 - 1}{3 - 1}$

$\: \: \: \: \: 1$