Question

Find the value of Sin18° + Cos 36°​

Answer 1

Answer:

−0.8291132

Answer's here

Answer 2

Answer:

sin⁡18∘−cos⁡36∘=sin⁡18∘−(1–2sin2⁡18∘)=sin⁡18∘−1+2sin2⁡18∘" role="presentation" style="margin: 0px; padding: 0px; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 15px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">sin18∘−cos36∘=sin18∘−(1–2sin218∘)=sin18∘−1+2sin218∘sin⁡18∘−cos⁡36∘=sin⁡18∘−(1–2sin2⁡18∘)=sin⁡18∘−1+2sin2⁡18∘

We know that…

sin⁡18∘=−1+54" role="presentation" style="margin: 0px; padding: 0px; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 15px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">sin18∘=−1+5–√4sin⁡18∘=−1+54

[If you want to know why Neil Morrison's answer to How do you determine the exact value (in radical form) of the sin 18 degrees? ]

sin⁡18∘−cos⁡36∘=−1+54−1+2(−1+54)2=−1+54−1+2(6–2516)=−1+5–4+3−54=−12" role="presentation" style="margin: 0px; padding: 0px; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 15px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">sin18∘−cos36∘=−1+5–√4−1+2(−1+5–√4)2=−1+5–√4−1+2(6–25–√16)=−1+5–√–4+3−5–√4=−12