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The solution of the equation is possible if
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a
k∈(−∞,4]
b
k∈(−∞,∞)
c
k∈[4,∞)
d
None of the above
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Correct option is A
Here, k cos x - 3 sin x = k +1 could be rewritten askk2+9cosx−3k2+9sinx=k+1k2+9⇒ cos(x+ϕ)=k+1k2+9where cosϕ=kk2+9and sinϕ=3k2+9which posses solution only, if−1≤k+1k2+9≤1⇒k+1k2+9≤1⇒(k+1)2≤k2+9⇒k2+2k+1≤k2+9⇒k≤4Hence, the interval in which kcos x - 3sin x = k +1 admits solution for k is (−∞,4]
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