What is the value of (cos(60)+cos(30))/(csc^2(30)+sin^2(45)) ?

The value of (cos(60)+cos(30))/(csc^2(30)+sin^2(45)) is (1+sqrt(3))/9

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(cos(60)+cos(30))/(csc^2(30)+sin^2(45))

\frac{cos ( 6 0 ^{\circ} ) + cos ( 3 0 ^{\circ} )}{csc ^{2} ( 3 0 ^{\circ} ) + sin ^{2} ( 4 5 ^{\circ} )}

\frac{1 + 3}{9}

Solution steps

\frac{cos ( 6 0 ^{\circ} ) + cos ( 3 0 ^{\circ} )}{csc ^{2} ( 3 0 ^{\circ} ) + sin ^{2} ( 4 5 ^{\circ} )}

Use the following trivial identity:

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

Use the following trivial identity:

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

Use the following trivial identity:

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

Use the following trivial identity:

sin (4 5^{\circ}) = \frac{2}{2}

= \frac{\frac{1}{2} + \frac{3}{2}}{2 ^{2} + ( \frac{2}{2} ) ^{2}}

Simplify

\frac{\frac{1}{2} + \frac{3}{2}}{2 ^{2} + ( \frac{2}{2} ) ^{2}} : \frac{1 + 3}{9}

= \frac{1 + 3}{9}

- e^{l n (c o s (2)) + 1} + e

60 cos (4 5^{\circ}) - 70 sin (6 0^{\circ}) - 50 sin (4 5^{\circ})

tan^{2} (6 0^{\circ}) - 3 cot^{2} (6 0^{\circ})

20 \cdot sin (2 5^{\circ})

5.9 tan (5 9^{\circ})

What is the value of (cos(60)+cos(30))/(csc^2(30)+sin^2(45)) ?
The value of (cos(60)+cos(30))/(csc^2(30)+sin^2(45)) is (1+sqrt(3))/9