Question

Sin 780.sin 480+cos 240.cos 300 =1/2

Answer 1

Answer:

Answer is 1/2

Step-by-step explanation:

sin780°

= sin(720°+60°)

= sin60°

= √3/2

sin480°

= sin(360°+120°)

= sin120°

=√3/2

cos240°

= cos(180°+60°)

= - cos60°

= -(1/2)

cos 300°

= cos(360°-60°)

= cos60°

= 1/2

Now

sin 780° . sin 480° + cos 240° . cos 300°

= (√3/2)(√3/2) - (1/2) (1/2)

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

= 2/4

=1/2

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Answer 2

Answer:

1/2

Step-by-step explanation:

LHS=sin780.sin480+cps240.cos300

sin780=sin(4π+60)

= sin60

=√3/2

sin480=sin(2π+120)

=sin120

=sin(180-60)

=sin60

=√3/2

cos240=cos(180+60)

= -cos60

= -1/2

cos300=cos(360-60)

=cos60

=1/2

substitute in problem

then. = √3/2×√3/2+(-1/2)×(1/2)

= 3/4-1/4

=3-1/4

=2/4

=1/2