Question

Sin15°的值,要保留根号正弦,余弦,正切,余切全部讲一下,

Answer 1

cos30=2cos15²-1=1-2sin²15=√3/2

所以cos²15=(√3+2)/4

=(8+4√3)/16

=(6+2√12+2)/16

=(√6+√2)²/16

cos15>0

所以cos15=(√6+√2)/4

1-2sin²15=√3/2

sin15=(2-√3)/4

=(8-4√3)/16

=(6-2√12+2)/16

=(√6-√2)²/16

sin15>0

所以sin15=(√6-√2)/4

tan15=sin15/cos15=(√6-√2)/(√6+√2)=2-√3

cot15=cos15/sin15=(√6+√2)/(√6-√2)=2+√3