What is the value of csc(510)-4cos(1020)+cos(0) ?

The value of csc(510)-4cos(1020)+cos(0) is 1

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csc(510)-4cos(1020)+cos(0)

csc (51 0^{\circ}) - 4 cos (102 0^{\circ}) + cos (0^{\circ})

1

Solution steps

csc (51 0^{\circ}) - 4 cos (102 0^{\circ}) + cos (0)

csc (51 0^{\circ}) = csc (15 0^{\circ})

= csc (15 0^{\circ}) - 4 cos (102 0^{\circ}) + cos (0)

cos (102 0^{\circ}) = cos (30 0^{\circ})

= csc (15 0^{\circ}) - 4 cos (30 0^{\circ}) + cos (0)

Rewrite using trig identities:

csc (15 0^{\circ}) = 2

Rewrite using trig identities:

cos (30 0^{\circ}) = \frac{1}{2}

Use the following trivial identity:

cos (0) = 1

= 2 - 4 \cdot \frac{1}{2} + 1

Simplify

2 - 4 \cdot \frac{1}{2} + 1 : 1

= 1

arccos (\frac{1}{7})

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

arcsinh (5)

arcsinh (2)

5 cos^{2} (0)

What is the value of csc(510)-4cos(1020)+cos(0) ?
The value of csc(510)-4cos(1020)+cos(0) is 1