= tan 70×cos 10×(tan 60×tan 20- 1)

= tan 70×cos 10×[(sin 60×sin 20/cos 60×cos 20)- 1]

= tan 70×cos 10×(sin 60×sin 20-cos 60×cos 20)/(cos 60×cos 20)

= tan 70×cos 10×[-cos(60+20)]/(cos 60×cos 20)

=-tan 70×cos 10×cos 80/(cos 60×cos 20)

=-tan 70×cos 10×sin 10/(cos 60×cos 20)

=-(sin 70/cos 70)×( 1/2)×sin 20/(cos 60×cos 20)

=-(cos 20/sin 20)×sin 20/(2 cos 60×cos 20)

=- 1/(2cos60)

=- 1