Question

6. The range of sina x + 4 sin x + 7 is 1. [1, 9] 2. [4, 12] 3. [1, 4] 4. [9, 12]​

Answer 1

Answer:

Given equation

sinx4+1−sinx1=a    ....(1)

f(x)=sinx4+1−sinx1

f′(x)=cosx((1−sinx)21−sin2x4)

=cosxsin2x(1−sinx)2(2−sinx)(3sinx−2)

For maxima or minima, f′(x)=0

⇒sinx=2(not possible) , sinx=32 and cosx=0⇒x=2π

⇒x=sin−132

f(sin−132)=6+3=9

f(0+)→