What is the value of sin(90)+(cos(210)+sin(300))^2+sec(240) ?

The value of sin(90)+(cos(210)+sin(300))^2+sec(240) is 2

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sin(90)+(cos(210)+sin(300))^2+sec(240)

sin (9 0^{\circ}) + (cos (21 0^{\circ}) + sin (30 0^{\circ}))^{2} + sec (24 0^{\circ})

2

Solution steps

sin (9 0^{\circ}) + (cos (21 0^{\circ}) + sin (30 0^{\circ}))^{2} + sec (24 0^{\circ})

Use the following trivial identity:

sin (9 0^{\circ}) = 1

Rewrite using trig identities:

cos (21 0^{\circ}) = - \frac{3}{2}

Rewrite using trig identities:

sin (30 0^{\circ}) = - \frac{3}{2}

Rewrite using trig identities:

sec (24 0^{\circ}) = - 2

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

Simplify

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

= 2

arctan (3) - arctan (2)

3 cos (21 0^{\circ})

600 cos (4 5^{\circ})

2 sin (112. 5^{\circ}) cos (112. 5^{\circ})

tan (\frac{7 π}{6} + \frac{π}{4})

What is the value of sin(90)+(cos(210)+sin(300))^2+sec(240) ?
The value of sin(90)+(cos(210)+sin(300))^2+sec(240) is 2