Question

prove that sin^(2)15°+sin 75°=1​

Answer 1

Answer:

I assume you are seeking 2(sin15∘+sin75∘)2 . There are many ways to do this: one way is to use the trigonometric sum formulas.

sin75∘=sin(30∘+45∘)=sin30∘cos45∘+cos30∘sin45∘=(12)(2√2)+(3√2)(2√2)=6√+2√4 .

We also have sin15∘=6√−2√4 , which can be found through either a similar argument or the fact that sin15∘=cos75∘=1−sin275∘−−−−−−−−−√ .

With that, 2(sin15∘+sin75∘)2=2(6√−2√4+6√+2√4)2=2(6√2)2=2⋅64=3 .