What is the value of sqrt(1+tan^2(45)) ?

The value of sqrt(1+tan^2(45)) is square root of 2

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sqrt(1+tan^2(45))

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

2

Solution steps

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

Use the following trivial identity:

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

= 1 + 1^{2}

Simplify

= 2

0.099 (9.8) (cos (2 2^{\circ})) + 0.71 (cos (6 8^{\circ}))

cos (\frac{2 π}{15}) cos (\frac{π}{30}) - sin (\frac{2 π}{15}) sin (\frac{π}{30})

\frac{28}{tan ( \frac{7 π}{18} )}

\frac{120 sin ( 8 )}{30}

arcsin (\frac{( 2 \cdot 5.8 \cdot 1 0 ^{- 7} )}{5.3 \cdot 1 0 ^{- 4}})

What is the value of sqrt(1+tan^2(45)) ?
The value of sqrt(1+tan^2(45)) is square root of 2