What is the value of (sin(30)+csc(30))/(sin^2(30)+cos^2(60)) ?

The value of (sin(30)+csc(30))/(sin^2(30)+cos^2(60)) is 5

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(sin(30)+csc(30))/(sin^2(30)+cos^2(60))

\frac{sin ( 3 0 ^{\circ} ) + csc ( 3 0 ^{\circ} )}{sin ^{2} ( 3 0 ^{\circ} ) + cos ^{2} ( 6 0 ^{\circ} )}

5

Solution steps

\frac{sin ( 3 0 ^{\circ} ) + csc ( 3 0 ^{\circ} )}{sin ^{2} ( 3 0 ^{\circ} ) + cos ^{2} ( 6 0 ^{\circ} )}

Use the following trivial identity:

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

Use the following trivial identity:

csc (3 0^{\circ}) = 2

Use the following trivial identity:

cos (6 0^{\circ}) = \frac{1}{2}

= \frac{\frac{1}{2} + 2}{( \frac{1}{2} ) ^{2} + ( \frac{1}{2} ) ^{2}}

Simplify

\frac{\frac{1}{2} + 2}{( \frac{1}{2} ) ^{2} + ( \frac{1}{2} ) ^{2}} : 5

= 5

\frac{cos ( 1 2 ^{\circ} )}{1.17}

8 \cdot cos^{2} (3 0^{\circ})

arctan (\frac{- 5}{- 7})

14 \cdot sin (4 5^{\circ})

\frac{1}{π} sin (π)

What is the value of (sin(30)+csc(30))/(sin^2(30)+cos^2(60)) ?
The value of (sin(30)+csc(30))/(sin^2(30)+cos^2(60)) is 5