if theta = 45 degree then verify sin2theta=2sintheta*costheta and cos2theta= cos​2theta-sin2theta

We have,θ = 45°i.LHS = sin 2θ = sin 2×45° = sin 90° = 1RHS = 2 sin θ . cos θ = 2 sin 45° . cos 45° = 2 ×12×12 = 1So, LHS = RHSHence,  sin 2θ  = 2 sin θ . cos θ ii.LHS = cos 2θ = cos 2×45° = cos 90° = 0RHS = cos2θ - sin2θ = cos245° - sin245° = 122 - 122 = 12 - 12 = 0So, LHS = RHSHence, cos 2θ =  cos2θ - sin2θ

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=>sin90 = 2sin45.cos45 and cos90 = cos​​245 - sin245
=1=  2/root 2 x root 2 and 0 = 1/root 2 - 1/root 2
= 1=1 and 0 = 0
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Hence the relationship is verified
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