What is the value of tan(20)-(cos(70))/(cos(20)) ?

The value of tan(20)-(cos(70))/(cos(20)) is 0

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tan(20)-(cos(70))/(cos(20))

tan (2 0^{\circ}) - \frac{cos ( 7 0 ^{\circ} )}{cos ( 2 0 ^{\circ} )}

0

Solution steps

tan (2 0^{\circ}) - \frac{cos ( 7 0 ^{\circ} )}{cos ( 2 0 ^{\circ} )}

Simplify

= \frac{tan ( 2 0 ^{\circ} ) cos ( 2 0 ^{\circ} ) - cos ( 7 0 ^{\circ} )}{cos ( 2 0 ^{\circ} )}

Rewrite using trig identities:

cos (7 0^{\circ}) = sin (2 0^{\circ})

cos (7 0^{\circ})

Use the following identity:

cos (x) = sin (9 0^{\circ} - x)

= sin (9 0^{\circ} - 7 0^{\circ})

Simplify

= sin (2 0^{\circ})

= \frac{tan ( 2 0 ^{\circ} ) cos ( 2 0 ^{\circ} ) - sin ( 2 0 ^{\circ} )}{cos ( 2 0 ^{\circ} )}

Rewrite using trig identities:

tan (2 0^{\circ}) = \frac{sin ( 2 0 ^{\circ} )}{cos ( 2 0 ^{\circ} )}

tan (2 0^{\circ})

Use the basic trigonometric identity:

tan (x) = \frac{sin ( x )}{cos ( x )}

= \frac{sin ( 2 0 ^{\circ} )}{cos ( 2 0 ^{\circ} )}

= \frac{\frac{s i n ( 2 0 ^{\circ} )}{c o s ( 2 0 ^{\circ} )} cos ( 2 0 ^{\circ} ) - sin ( 2 0 ^{\circ} )}{cos ( 2 0 ^{\circ} )}

Simplify

= 0

sec (16 5^{\circ})

3 sin (- \frac{10 π}{7}) csc (- \frac{24 π}{7})

sin (9 9^{\circ})

arctan (1000)

50 cos (4 5^{\circ})

What is the value of tan(20)-(cos(70))/(cos(20)) ?
The value of tan(20)-(cos(70))/(cos(20)) is 0