Explanation
sinx+2sin2x−sin3x=3
sinx+4sinxcosx−3sinx+4sin3x=3
sinx[−2+4cosx+4(1−cos2x)]=3
sinx[2−(4cos2x−4cosx+1)+1]=3
sinx[3−(2cosx−1)2]=3
⇒sinx=1 and 2cosx−1=0
⇒x=π2 and x=π3
Which is not possible at same time.
Hence, no solution.
Consider the given expression,
sec2α+cos2α
AS it is clear that cos2α and sec2α are positive numbers
So, we can apply the theorem of A.M and G.M
A.M>=G.M
so we have
(sec2α+cos2α2)=√sec2α+cos2α
Or sec2α+cos2α=2√sec2α+cos2α=2.1
sec2α+cos2α=2
So, minimum value of sec2α+cos2α is 2.
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