How to prove this tangent identities?

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

#HelpMe! #MathProblem

Easy Math Editor

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Comments

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

Pi Han Goh - 7 years, 7 months ago

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 :)

Leonardo Chandra - 7 years, 7 months ago

Tan40°+tan5°+tan40°×tan5°=1 prove it

Rahul Prajapati - 5 years, 9 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$