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Question : 20 of 160
Marks:
+1,
-0
Solution:
Given,
‌cos‌θ−sin‌θ=√5sin‌θ‌⇒‌‌(cos‌θ−sin‌θ)2=5sin‌2θ‌⇒cos2θ+sin‌2θ−2sin‌θ‌cos‌θ=5sin‌2θ
‌⇒‌‌2sin‌θ‌cos‌θ=1−5sin‌2θ.....(i)
Now,
cos‌θ+4sin‌θ=√(cos‌θ+4sin‌θ)2‌‌=√cos2θ+16sin‌2θ+8sin‌θ‌cos‌θ‌‌=√cos2θ+16sin‌2θ+4−20sin‌2θ‌[∵‌ using ‌Eq.(i)]‌‌=√cos2θ−4sin‌2θ+4‌‌=√cos2θ−4(1−cos2θ)+4‌‌=√cos2θ+4cos2θ‌‌=√5‌cos‌θ
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