This is the basic and conceptual question from trigonometry (trigonometric ratios) in which we have to find the value of cos 60° cos 30° + sin 30° sin 60°
RS Aggarwal, Class 10, chapter 11, question no 2.
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Use sin(90∘−θ)=cosθ and cos(90∘−θ)=sinθ
and cos2θ+sin2θ=1
Now,
sin30∘⋅cos60∘+cos30∘⋅sin60∘
=sin(90∘−60∘)⋅cos60∘+cos(90∘−60∘)⋅sin60∘
=cos60∘⋅cos60∘+sin60∘⋅sin60∘
=cos^2 60°+sin^2 60°
=1