What is the value of tan^2(240)+sec^2(225) ?

The value of tan^2(240)+sec^2(225) is 5

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tan^2(240)+sec^2(225)

tan^{2} (24 0^{\circ}) + sec^{2} (22 5^{\circ})

5

Solution steps

tan^{2} (24 0^{\circ}) + sec^{2} (22 5^{\circ})

tan (24 0^{\circ}) = tan (6 0^{\circ})

= tan^{2} (6 0^{\circ}) + sec^{2} (22 5^{\circ})

Rewrite using trig identities:

sec^{2} (22 5^{\circ}) = tan^{2} (4 5^{\circ}) + 1

= tan^{2} (6 0^{\circ}) + tan^{2} (4 5^{\circ}) + 1

Use the following trivial identity:

tan (6 0^{\circ}) = 3

Use the following trivial identity:

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

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

Simplify

(3)^{2} + 1^{2} + 1 : 5

= 5

70 cos (3 0^{\circ})

1 + 2 cos (\frac{π}{3})

arctan (56)

sin (\frac{π}{4}) \cdot sin (\frac{π}{4})

ln (2 + tan (\frac{π}{32}))

What is the value of tan^2(240)+sec^2(225) ?
The value of tan^2(240)+sec^2(225) is 5