What is the value of cos(400)sec(40) ?

The value of cos(400)sec(40) is 1

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cos(400)sec(40)

cos (40 0^{\circ}) sec (4 0^{\circ})

1

Solution steps

cos (40 0^{\circ}) sec (4 0^{\circ})

cos (40 0^{\circ}) = cos (4 0^{\circ})

cos (40 0^{\circ})

Rewrite

40 0^{\circ}

36 0^{\circ} + 4 0^{\circ}

= cos (36 0^{\circ} + 4 0^{\circ})

Apply the periodicity of

cos

cos (x + 36 0^{\circ}) = cos (x)

cos (36 0^{\circ} + 4 0^{\circ}) = cos (4 0^{\circ})

= cos (4 0^{\circ})

= cos (4 0^{\circ}) sec (4 0^{\circ})

Rewrite using trig identities:

cos (4 0^{\circ}) = \frac{1}{sec ( 4 0 ^{\circ} )}

cos (4 0^{\circ})

Use the basic trigonometric identity:

cos (x) = \frac{1}{sec ( x )}

= \frac{1}{sec ( 4 0 ^{\circ} )}

= \frac{1}{sec ( 4 0 ^{\circ} )} sec (4 0^{\circ})

Simplify

= 1

10 sin (5 0^{\circ})

csc (\frac{- 11 π}{6})

6 \cdot sin (3 0^{\circ})

cos^{2} (3 2^{\circ}) - sin^{2} (3 2^{\circ})

arctan (\frac{6.1}{5.1})