Question

without using trigonometric table,
proven that
tan 35
tan 40, tan 45 tan 50, tan 35=1.​

Answer 1

Step-by-step explanation:

We use the identity

tan

(

a

−

b

)

=

tan

a

−

tan

b

1

+

tan

a

tan

b

And the fact

45

=

35

−

10

. and

tan

45

=

1

. Then

tan

35

=

tan

(

45

−

10

)

=

tan

45

−

tan

10

1

+

tan

45

tan

10

=

=

1

−

tan

10

1

+

tan

10

. Transposing terms, we have

tan

35

(

1

+

tan

10

)

=

1

−

tan

10

tan

35

+

tan

35

tan

10

+

tan

10

1

QED

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