Question

10. Sin? 0 + cos' 0 - (sin 0 + cos 0) (1 - sin 0 cos 6).​

Answer 1

Answer:

Text Solution

f(0)= 0 has exactly 2 real solutions in [0,π]

[0,π]

f(0) =0 has exactly 3 real solutions in [0,π]

[0,π]

range of function

f(0)

1−sin20

is

[−2–√,2–√]

f(0)1-sin20 is [-2,2]

range of fucntion .

f(0)

sin20−1

is [−3,3] is [−3,3]

f(0)sin20-1 is [-3,3] is [-3,3]

Answer :

A::C

Solution :

f(0)=

sin 3

0+

cos 3

0−cos0sin0(sin0+cos0)

f(0)=sin30+cos30-cos0sin0(sin0+cos0)

=

(sin0+cos0) 3

−4sin0cos0(sin0+sin0)

=(sin0+cos0)3-4sin0cos0(sin0+sin0)

=(sin0+cos0)[1−sin20]

=(sin0+cos0)[1-sin20]

Nowf(0)=0

Nowf(0)=0

⇒tan0=−1 or sin20=1

⇒tan0=-1 or sin20=1

⇒f(0)=0

⇒f(0)=0

has 2 real solutions in [0,π]

[0,π]