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Alisiya [41]
3 years ago
9

8. Evaluate: f(x) = x2 + 1 g(x) = 5 - x a. (f+g)(x) = b. (f-g)(x) =

Mathematics
1 answer:
Papessa [141]3 years ago
6 0

Answer:

(f+g)(x)=2x+1+5 - x

(f+g)(x)=x + 6

(f - g)(x)= 2x + 1 - (5- x )

(f - g)(x)= 3x - 4

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Answer:

Correct option is

B

0

D

−1

sinx+sin2x+sin3x

=sin(2x−x)+sin2x+sin(2x+x)

=2sin2xcosx+sin2x [ by using sin(A+B)=sinAcosB+sinBcosA and sin(A−B)=sinAcosB−sinBcosA ]

=sin2x(2cosx+1)........(i)

cosx+cos2x+cos3x

=cos(2x−x)+cos2x+cos(2x+x)

=2cos2xcosx+cos2x [By using cos(a−b)=cosa⋅cosb+sina⋅sinb and cos(a+b)=cosa⋅cosb−sina⋅sinb]

=cos2x(2cosx+1).....(ii)

∴(sinx+sin2x+sin3x)

2

+(cosx+cos2x+cos3x)

2

=1

sin

2

2x(2cosx+1)

2

+cos

2

2x(2cosx+1)

2

=1.......[From(i)(ii)]

⇒(2cosx+1)

2

=1

⇒2cosx+1=±1

∴cosx=0or−1

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