What is the value of sec^2(45)-2tan^2(45) ?

The value of sec^2(45)-2tan^2(45) is 0

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sec^2(45)-2tan^2(45)

sec^{2} (4 5^{\circ}) - 2 tan^{2} (4 5^{\circ})

0

Solution steps

sec^{2} (4 5^{\circ}) - 2 tan^{2} (4 5^{\circ})

Use the following trivial identity:

sec (4 5^{\circ}) = 2

sec (4 5^{\circ})

sec (x)

periodicity table with

36 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} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

= 2

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

= (2)^{2} - 2 \cdot 1^{2}

Simplify

(2)^{2} - 2 \cdot 1^{2} : 0

(2)^{2} - 2 \cdot 1^{2}

Apply rule

1^{a} = 1

1^{2} = 1

= (2)^{2} - 2 \cdot 1

(2)^{2} = 2

(2)^{2}

Apply radical rule:

a = a^{\frac{1}{2}}

= (2^{\frac{1}{2}})^{2}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= 2^{\frac{1}{2} \cdot 2}

\frac{1}{2} \cdot 2 = 1

\frac{1}{2} \cdot 2

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 2}{2}

Cancel the common factor:

2

= 1

= 2

2 \cdot 1 = 2

2 \cdot 1

Multiply the numbers:

2 \cdot 1 = 2

= 2

= 2 - 2

Subtract the numbers:

2 - 2 = 0

= 0

= 0

cos (\frac{8 π}{2})

2 cos (16 0^{\circ})

cos (2) (45)

3 \cdot cos (2 0^{\circ})

cot (4 0^{\circ}) - \frac{sin ( 5 0 ^{\circ} )}{sin ( 4 0 ^{\circ} )}

What is the value of sec^2(45)-2tan^2(45) ?
The value of sec^2(45)-2tan^2(45) is 0