Question

. (a) cos(x + y) + cos(x - y) = ...
(6) Prove that cos ( + x) + cos C. - x) = VZ cos x​

Answer 1

Answer:

Correct option is

D

±

2

Since cos(x−y),cosx,cos(x+y) are in H.P

We have

cosx=

cos(x−y)+cos(x+y)

2cos(x−y)cos(x+y)

=

2cosxcosy

2(cos

2

x−sin

2

y)

⇒cos

2

xcosy=cos

2

x−sin

2

y

⇒(1−cosy)cos

2

x=sin

2

y

⇒cos

2

x=

1−cosy

sin

2

y

=

2sin

2

(

2

y

)

4sin

2

(

2

y

)cos

2

(

2

y

)

⇒cos

2

x=2cos

2

(

2

y

)⇒cosxsec(

2

y

)=±

2

Answer 2

Answer:

$\sqrt{2}$

Step-by-step explanation:

Since cos(x−y),cosx,cos(x+y) are in H.P

We have

cosx=

cos(x−y)+cos(x+y)

2cos(x−y)cos(x+y)

=

2cosxcosy

2(cos

2

x−sin

2

y)

⇒cos

2

xcosy=cos

2

x−sin

2

y

⇒(1−cosy)cos

2

x=sin

2

y

⇒cos

2

x=

1−cosy

sin

2

y

=

2sin

2

(

2

y

)

4sin

2

(

2

y

)cos

2

(

2

y

)

⇒cos

2

x=2cos

2

(

2

y

)⇒cosxsec(

2

y

)=±

2