cos‌α+sin‌α=√2‌cos‌α On squaring both sides, we get: cos2α+sin2α+2‌sin‌α‌cos‌α=2cos2α 1+2‌sin‌α‌cos‌α=2cos2α 2‌sin‌α‌cos‌α=2cos2α−1 Now, cos‌α−sin‌α=√sin2α+cos2α−2‌sin‌α‌cos‌α =√1−2cos2α+1=√2‌sin‌α