Thread: can you please help me with this high school trigonometry problem?

we took down a note, where the example showed us how to find the exact value of

tan (-5π / 12)

then she wrote down....

tan (-π/4) - tan (π/6)
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
1+tan(-π/4)tan(π/6)


and then from that, she jumped to the final answer, which is...

(-√3-1) / (-√3-1)

How did she do that?
Maybe I copied down her note wrong, cuz I keep getting a different answer...

Originally Posted by lanvin

we took down a note, where the example showed us how to find the exact value of

tan (-5π / 12)

then she wrote down....

tan (-π/4) - tan (π/6)
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
1+tan(-π/4)tan(π/6)


and then from that, she jumped to the final answer, which is...

(-√3-1) / (-√3-1)

How did she do that?
Maybe I copied down her note wrong, cuz I keep getting a different answer...

Using a reference angle we see that it is an angle of 75 degrees

So now sum difference formula for tan





Then multiply by 3 to numerator and denominator



then rationalize





Now multiply a neg in because it is in the 4th quad