Question

Find the value of x in each of the following : cos 2x = cos 60° cos 30° + sin 60° sin 30°

Answer 1

hello....

Cos 2x = Cos 60×Cos 30 +Sin 60×Sin 30

Cos 2x = Cos (60-30)

Cos 2x= Cos 30

2x=30

x= 15...

thank you

Answer 2

SOLUTION :

Given :  

cos 2x = cos 60°cos 30° + sin 60°sin 30°

cos 2x = ½ × √3/2 + √3/2 × 1/2

[cos 60° = ½,  sin 30° = ½ , sin 60° = cos 30° = √3/2]

cos 2x = √3/4 + √3/4

cos 2x = (√3 +√3)/4

cos 2x = 2√3 /4

cos 2x = √3/2

cos 2x = cos 30°

[cos 30° = √3/2]

2x = 30°

x = 30/2 = 15°

x = 15°

Hence, the value of x  is 15°.

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