Question

find the value of cos75 ×cos15_sin75×sin15​

Answer 1

Answer:

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Answer 2

Method 1

Use:

   cos(α−β)=cos(α)cos(β)−sin(α)sin(β)

So:

   cos75∘cos15∘+sin75∘sin15∘=cos(75∘−15∘)=cos60∘=12

Method 2

Use:

   cos(θ)=sin(90∘−θ)

   sin(θ)=cos(90∘−θ)

   sin(2θ)=2sinθcosθ

So:

   cos75∘cos15∘+sin75∘sin15∘=sin15∘cos15∘+sin15∘cos15∘=sin30∘=12