Question

Evaluate each of the following sin 45° sin 30° + cos 45° cos 30°

Answer 1

SOLUTION :  

Given :  

Sin 45° sin 30°  + cos 45° cos 30°                                                      

= 1/√2 × ½ + 1/√2 × √3/2

= 1/2√2 + √3 / 2√2

Sin 45° sin 30° + cos 45° cos 30° = (1 +√3)/ 2√2

[ sin 45° = 1/√2 ,  sin 30° = ½  , cos 45° = 1/√2  ,cos 30° = √3/2 ] 

Hence, Sin 45° sin 30°  + cos 45° cos 30° = (1 +√3)/ 2√2 .

HOPE THIS ANSWER WILL HELP YOU

Answer 2

Sin 45° = 1/√2
Sin 30° = 1/2
Cos 45° = 1/√2
Cos 30° = √3/2
Now replace the values
1/√2 × 1/2 + 1/√2 × √3/2
1/2√2 + √3/2/2
1+√3 / 2√2