Question

What is the value of sin²18° + cos²882°? TRY ANSWERING AND DONT ANSWER IF YOU DON'T KNOW, NO ONE IS GOING TO MARK YOU AS BRAINLIEST WHEN YOU DONT HAVE A BRAIN​

Answer 1

Step-by-step explanation:

So, we will first expand the binomial:

(sinx+cosx)2=sin2x+2sinxcosx+cos2x  

Since  sin2x+cos2x=1  we can write the expression as  1+2sinxcosx.  

Now,  2sinxcosx  is not easier to compute than  sinx+cosx , but we can “metamorphose” it into something easier!

Perhaps you know the trigonometric identity  sin(x+y)=sinxcosy+sinycosx . Let’s see what happens when  x=y .

sin(2x)=sinxcosx+sinxcosx=2sinxcosx.  

So in fact  1+2sinxcosx=1+sin2x !

Now, by plugging in  x=18∘  we get  (sin18∘+cos18∘)2=1+sin36∘ .

Since  36∘  is roughly close to  30∘  we can make the very rough approximation of  sin36∘≈sin30∘=12 . So  1+sin36∘≈32.  

(If you want to know the exact value,  sin36∘=0.58 , so the expression is equal to  1.58 )

Hope it helps you!!!!!