Question

sin 480° cos 690° + cos 780° sin 1050°​

Answer 1

Step-by-step explanation:

Given :-

sin 480° cos 690° + cos 780° sin 1050°

Sin (360°+120°) Cos (720°-30°)+cos(720°+60°) sin (1080°-30°)

=>Sin(360°+120°) Cos (2×360°-30°) +

cos(2×360°+60°)sin(3×360°-30°)

we know that

Sin(360+A)=Sin A

Cos(360°+A)=CosA

Sin(360°-A)=- SinA

Cos(360°-A)=Cos A

now,

=>Sin120°Cos30°+Cos60°+(-Sin30°)

=>Sin(90+30°)Cos30°+Cos60°(-Sin30°)

we know that

Sin (90+A)=CosA

=>Cos30°Cos30°+Cos60°(-Sin30°)

=>Cos² 30°-Cos 60°Sin30°

=>(√3/2)²-(1/2)(1/2)

=>(3/4)-(1/4)

=>(3-1)/4

=>2/4

=>1/2

sin 480° cos 690° + cos 780° sin 1050°=1/2