Question

(vi) 2 sin 135/2 °
cos 45/2°
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Answer 1

Answer

Assertion is true as

x=sin(α−β)sin(γ−β)=(sinαcosβ−cosαsinbeta)(sinγcosδ−cosγsinδ)

=sinαcosβsinγcosδ−sinαcosβcosγsinδ−cosαsinβsinγcosγ+cosαsinβcosγsinδ

y=sin(β−γ)sin(α−δ)=(sinβcosγ−cosβsinγ)(sinαcosδ−cosαsinγ)

=sinαsinβcosγcosδ−cosαsinβcosγsinδ−sinαcosβsinγcosδ+cosαcosβsinγsinδ

z=sin(γ−α)sin(β−γ)=(sinγcosα−cosγsinα)(sinβcosδ−cosβsinδ)

=cosαsinβsinγcosδ−cosαcosβsinγsinδ−sinαsinβcosγcosδ+sinαcosβcosγsinδ

x+y+z=0

Reason is false as

2sinAsinB=cos(A−B)−cos(A+B)

Step-by-step explanation:

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