Question

Show that 1-cos theta 1+cos theta=cosec theta- cot theta

Answer 1

Answer:

(1+cos

9

π

)(1+cos

9

3π

)(1+cos

9

5π

)(1+cos

9

7π

)

Using formulae.

1+cos2θ=2cos

2

θ

2cos

2

18

π

.2cos

2

18

3π

.2cos

2

18

5π

.2cos

2

18

7π

=16cos

2

10

∘

.cos

2

30

∘

.cos

2

50

∘

.cos

2−

70

∘

=16(

2

3

)

2

[cos

2

10.cos

2

50.cos

2−

70]

Using formulae.

cosx.cos(60+x)cos(60−x)=

4

cos3x

16×

4

3

[cos10.cos50.cos70]

2

=12[cos

4

3×10

]

2

=

16

12

×

4

3

=

16

9