Trig question (1 Viewer)

[big_bang344]

Can someone help me with this question?

Evaluate: sin (45 - x) cos (45 - x)

I know it's easy but i just cant figure it out!

 

[stevey6404]

Can someone help me with this question?

Evaluate: sin (45 - x) cos (45 - x)


I know it's easy but i just cant figure it out!

Use the sin (a-b) rule and cos (a-b) rule?


= (sin45cosx - cos45sinx) (cos45cosx + sin45sinx)
= (1/root 2 cosx - 1/root 2 sinx) (1/root 2 cosx + 1/root 2 sinx)
= you can see it.

etc.

*shrugs* HSC's way too long ago.

 

[SpiralFlex]

Let's recall a famous identity,






We can apply this to the question. Let





Ah, we get a complementary angle!




If you are wondering...

What is a complementary angle?



----Understanding---- (Not part of proof)

Consider the following pretty diagram.





I will call the hypotenuse .

So from the diagram,

 

[BadMeetsEvil]

compound angle, i think that's what it's called, where you expand the double angle inside sin and cos

=(sin45cosx-cos45sinx)(cos45cosx+sin45sinx)

=(1/sqroot(2)cosx-1/sqroot(2)sinx)(1/sqroot(2)cosx+1/sqroot(2)sinx)

simplify it

you get

1/sqroot(2)(cosx-sinx)(cosx+sinx)

and difference between to squares

=1/sqroot(2)(cosx(squared)-sinx(squared))

 

[big_bang344]

Thanks Spi! And Badmeetsevil, are you playing CSS right now?

 

[BadMeetsEvil]

lol no and I don't play it