What is the value of 2sin(105)cos(105) ?

The value of 2sin(105)cos(105) is -1/2

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2sin(105)cos(105)

2 sin (10 5^{\circ}) cos (10 5^{\circ})

- \frac{1}{2}

Solution steps

2 sin (10 5^{\circ}) cos (10 5^{\circ})

Rewrite using trig identities:

sin (21 0^{\circ})

= sin (21 0^{\circ})

Rewrite using trig identities:

sin (18 0^{\circ}) cos (3 0^{\circ}) + cos (18 0^{\circ}) sin (3 0^{\circ})

= sin (18 0^{\circ}) cos (3 0^{\circ}) + cos (18 0^{\circ}) sin (3 0^{\circ})

Use the following trivial identity:

sin (18 0^{\circ}) = 0

Use the following trivial identity:

cos (3 0^{\circ}) = \frac{3}{2}

Use the following trivial identity:

cos (18 0^{\circ}) = (- 1)

Use the following trivial identity:

sin (3 0^{\circ}) = \frac{1}{2}

= 0 \cdot \frac{3}{2} + (- 1) \frac{1}{2}

Simplify

= - \frac{1}{2}

sec (arcsin (\frac{12}{13}))

1 + sin (\frac{π}{4})

2 (cos (3 0^{\circ}) + i sin (3 0^{\circ}))

tan (arcsin (\frac{7}{10}))

\frac{5}{cos ( 7 2 ^{\circ} )}