Question

Sin(pie/4+x).Sin(pie/4-x)=1/2cos x


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Answer 1

→π/4=(π/4×180/π)° = 45°

→sin(45°+x).sin(45°-x)

→[sin45°cosx+cos45°sinx][sin45°cosx-cos45°sinx]

→[1/√2cosx +1/√2sinx].[1/√2cosx-1/√2sinx]

→1/√2[cosx+sinx].1/√2[cosx-sinx]

→1/2 [cos²x-sin²x]

→1/2 [cos²x+sin²x - 2sin²x]

→1/2 × [1-2sin²x]

(¡ : cos²x = 1-2sin²x)

→1/2 cos²x

[In question, instead of ½cos x, there must be ½cos²x]

Answer 2

Solution !!

↪π/4=(π/4×180/π)° = 45°

↪sin(45°+x).sin(45°-x)

↪[sin45°cosx+cos45°sinx][sin45°cosx-cos45°sinx]

↪[1/√2cosx +1/√2sinx].[1/√2cosx-1/√2sinx]

↪1/√2[cosx+sinx].1/√2[cosx-sinx]

↪1/2 [cos²x-sin²x]

↪1/2 [cos²x+sin²x - 2sin²x]

↪1/2 × [1-2sin²x]

↪1/2 cos²x