Given that cos‌θ−4sin‌θ=1... (i) On squaring both sides of equation (i) ‌cos2θ+16sin‌2θ−8sin‌θ‌cos‌θ=1 ⇒15sin‌2θ−8sin‌θ‌cos‌θ=0 ⇒sin‌θ(15sin‌θ−8‌cos‌θ)=0 ⇒sin‌θ=0‌ or ‌tan‌θ=‌
8
15
but tan‌θ is not satisfy the equation (i) ‌∴‌‌sin‌θ=0 ‌⇒‌‌θ=0,π ‌‌ at ‌‌‌θ=0 ‌sin‌θ+4‌cos‌θ=0+4=4 ‌‌ at ‌‌θ=π ‌sin‌θ+4‌cos‌θ=0−4=−4 ‌