Question

Let x = sin 1° then 1 1 + cos 1° cos 20 cos 2° cos 30 1 + +. cos 30 COS 4° ​

Answer 1

Step-by-step explanation:

1

+

cos1

∘

.cos2

∘

1

+

cos2

∘

.cos3

∘

1

+...+

cos44

∘

.cos45

∘

1

=

x

1

(

cos0

∘

.cos1

∘

sin(1

0

−0

0

)

+

cos1

∘

.cos2

∘

sin(2

0

−1

0

)

+

cos2

∘

.cos3

∘

sin(3

0

−2

0

)

+...+

cos44

∘

.cos45

∘

sin(45

0

−44

0

)

)

=

x

1

(

cos0

∘

.cos1

∘

sin1

0

cos0

0

−cos1

0

sin0

0

+

cos1

∘

.cos2

∘

(sin2

0

cos1

0

−cos2

0

sin1

0

+

cos2

∘

.cos3

∘

sin3

0

cos2

0

−cos3

0

sin2

0

++

cos44

∘

.cos45

∘

sin45

0

cos44

0

−cos45

0

sin44

0

)sin(A−B)=sinAcosB−sinBcosA

=

x

1

(tan1

0

−tan0

0

+tan2

0

−tan1

0

+

+tan45

0

−tan44

0

)=

x

1

(tan45

0

−tan0

0

)= 1/x