What is the value of sin(20)-cos(70)+tan(45) ?

The value of sin(20)-cos(70)+tan(45) is 1

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sin(20)-cos(70)+tan(45)

sin (2 0^{\circ}) - cos (7 0^{\circ}) + tan (4 5^{\circ})

1

Solution steps

sin (2 0^{\circ}) - cos (7 0^{\circ}) + tan (4 5^{\circ})

Rewrite using trig identities:

sin (2 0^{\circ}) = cos (7 0^{\circ})

sin (2 0^{\circ})

Use the following identity:

sin (x) = cos (9 0^{\circ} - x)

= cos (9 0^{\circ} - 2 0^{\circ})

Simplify

= cos (7 0^{\circ})

= cos (7 0^{\circ}) - cos (7 0^{\circ}) + tan (4 5^{\circ})

Simplify

= tan (4 5^{\circ})

Use the following trivial identity:

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

tan (4 5^{\circ})

tan (x)

periodicity table with

18 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= 1

= 1

sin (- 3)

arctan (- 2.08)

10 \cdot tan (6 0^{\circ})

(- 2 sin (1 2^{\circ}))^{2} + cos^{2} (1 2^{\circ}) + 1

arccos (0.49038)

What is the value of sin(20)-cos(70)+tan(45) ?
The value of sin(20)-cos(70)+tan(45) is 1