What is the value of sin(30)tan(45)+tan(30)sin(60) ?

The value of sin(30)tan(45)+tan(30)sin(60) is 1

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sin(30)tan(45)+tan(30)sin(60)

sin (3 0^{\circ}) tan (4 5^{\circ}) + tan (3 0^{\circ}) sin (6 0^{\circ})

1

Solution steps

sin (3 0^{\circ}) tan (4 5^{\circ}) + tan (3 0^{\circ}) sin (6 0^{\circ})

Use the following trivial identity:

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

Use the following trivial identity:

tan (4 5^{\circ}) = 1

Use the following trivial identity:

tan (3 0^{\circ}) = \frac{3}{3}

Use the following trivial identity:

sin (6 0^{\circ}) = \frac{3}{2}

= \frac{1}{2} \cdot 1 + \frac{3}{3} \cdot \frac{3}{2}

Simplify

\frac{1}{2} \cdot 1 + \frac{3}{3} \cdot \frac{3}{2} : 1

= 1

cos (arctan (- 3)) + csc (arcsec (2))

sin (\frac{π}{3} - arctan (\frac{1}{3}))

5 + 4 cos (\frac{π}{3})

ln (tan (\frac{π}{4}))

\frac{cos ( \frac{π}{6} )}{( 1 - sin ( \frac{π}{6} ) ) ^{2}}

What is the value of sin(30)tan(45)+tan(30)sin(60) ?
The value of sin(30)tan(45)+tan(30)sin(60) is 1