Question

17. If sin a ,sin ß, sin y are in A.P and
cosa, cos B, cos y are in G.P then
cos’ a + cos² y - 4 cos a cos y
1-sin a sin y
is equal to
1) 2
2) 1
3)-2
4)-1​

Answer 1

ANSWER

Assume y=

1−sinα.sinγ

cos

2

α+cos

2

γ−4cosα.cosγ

since, sinα,sinβ,sinγ are in A.P ⇒2sinβ=sinα+sinγ

squaring, 4sin

2

β=sin

2

α+sin

2

γ+2sinα.sinγ=2−(cos

2

α+cos

2

γ)+2sinα.sinγ

and cosα,cosβ,cosγ are in G.P ⇒cos

2

β=cosα.cosγ

Using this equation,

y=

1+sinα.sinγ

cos

2

α+cos

2

γ−4cosα.cosγ

=

1+sinα.sinγ

2+2sinα.sinγ−4sin

2

β−4cos

2

β

=

1+sinα.sinγ

2+2sinα.sinγ

=2