Is 1+tan^2(3/4)=sec^2(x) ?

The answer to whether 1+tan^2(3/4)=sec^2(x) is False

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prove 1+tan^2(3/4)=sec^2(x)

prove

1 + tan^{2} (\frac{3}{4}) = sec^{2} (x)

False

Solution steps

1 + tan^{2} (\frac{3}{4}) = sec^{2} (x)

Show that the two sides are not equal

For

1 + tan^{2} (\frac{3}{4}) = sec^{2} (x)

plug in

x = 0

1 + tan^{2} (\frac{3}{4}) = 1.86787 \dots

1 + tan^{2} (\frac{3}{4})

Refine to a decimal form

= 1.86787 \dots

sec^{2} (0) = 1

sec^{2} (0)

Use the following trivial identity:

sec (0) = 1

sec (0)

sec (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

= 1

= 1^{2}

Simplify

= 1

The two sides are not equal

\Rightarrow False