Hi, brilliant users. I have a little problem again about trigonometry. it's all about tangent function. Here's the problem:

Prove that: tan 5.tan 40 - tan 10.tan 35 = tan 10 + tan 35 - tan 5 - tan 40

From where, I must started first? thanks

No vote yet

1 vote

×

Problem Loading...

Note Loading...

Set Loading...

## Comments

Sort by:

TopNewestHint: with, \(A+B = 45^\circ \), we have \( 1 = \tan (A+B) = \frac { \tan (A) + \tan (B) } {1 - \tan (A) \tan (B) } \)

Log in to reply

Thanks. I got it now. The key is your hint and operation at the right side:

We got: tan 10+tan 35 = tan 45

(1-tan 10.tan 35) and tan 5+tan 40= tan 45(1-tan 5.tan 40)So, the equation become:

tan 10+tan 35-(tan 5+tan 40)

= 1-tan 10.tan 35-(1-tan 5.tan 40)

= -tan 10.tan 35 +tan 5.tan 40

= tan 5.tan 40 - tan 10.tan 35 (proved)

Thanks, Pi Han :)

Log in to reply

Tan40°+tan5°+tan40°×tan5°=1 prove it

Log in to reply