What is the value of (3sin(36)+4cos(54))csc(36) ?

The value of (3sin(36)+4cos(54))csc(36) is 7

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(3sin(36)+4cos(54))csc(36)

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

7

Solution steps

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

Rewrite using trig identities:

csc (3 6^{\circ}) = \frac{1}{sin ( 3 6 ^{\circ} )}

= (3 sin (3 6^{\circ}) + 4 cos (5 4^{\circ})) \frac{1}{sin ( 3 6 ^{\circ} )}

Simplify

= \frac{3 sin ( 3 6 ^{\circ} ) + 4 cos ( 5 4 ^{\circ} )}{sin ( 3 6 ^{\circ} )}

Rewrite using trig identities:

sin (3 6^{\circ}) = \frac{2 5 - 5}{4}

Rewrite using trig identities:

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

= \frac{3 \cdot \frac{2 5 - 5}{4} + 4 \cdot \frac{2 5 - 5}{4}}{\frac{2 5 - 5}{4}}

Simplify

\frac{3 \cdot \frac{2 5 - 5}{4} + 4 \cdot \frac{2 5 - 5}{4}}{\frac{2 5 - 5}{4}} : 7

= 7

4 0^{2} + 6 0^{2} - 2 (40) (60) cos (15 5^{\circ})

6 sec^{2} (2 (\frac{π}{2}))

100 (cos (\frac{1}{5}) - cos (\frac{1}{10}))

e^{s i n (i)}

ln (cos (\frac{π}{6}))

What is the value of (3sin(36)+4cos(54))csc(36) ?
The value of (3sin(36)+4cos(54))csc(36) is 7