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Answers
Step-by-step explanation:
Given :-
Sin 750° Cos 300° + Cos 1470° Sin (-1020°)
To find:-
Find the value of the given expression?
Solution:-
Given that :-
Sin 750° Cos 300° + Cos 1470° Sin (-1020°)
Sin 750° can be written as
Sin 750° = Sin (720°+30°)
=> Sin 750° = Sin (2×360°+30°)
=> Sin 750° = Sin 30°
Since Sin (360°+A) = Sin A
and
Cos 300° = Cos (270°+30°)
=> Cos 300° = Sin 30°
Since Cos (270°+A) = Sin A
Cos 1470° = Cos (1440°+30°)
=> Cos 1470° = Cos (4×360°+30°)
=> Cos 1470° = Cos 30°
Since Cos (360°+A) = Cos A
and
Sin (-1020°) = - Sin 1020°
Since Sin (-A) = - Sin A
=> Sin 1020° = -[Sin (1080°-60°)]
=> Sin 1020° = -[Sin (3×360°-60°)]
=> Sin 1020° = -[- Sin 60°]
Since Sin (360°-A) = - Sin A
=> Sin (-1020°) = Sin 60°
Now given expression becomes
=> Sin 750° Cos 300° + Cos 1470° Sin (-1020°)
=> Sin 30° .Sin 30° + Cos 30°. Sin 60°
=> (1/2).(1/2) + (√3/2).(√3/2)
=> (1/4)+(√3×√3)/4
=> (1/4)+(3/4)
=> (1+3)/4
=> 4/4
=> 1
or
Sin 30° .Sin 30° + Cos 30°. Sin 60°
=> Sin² 30° + Cos 30° Sin (90°-30°)
=> Sin² 30° + Cos30° . Cos 30°
Since Sin (90°-A) = Cos A
=> Sin² 30° + Cos² 30°
We know that
Sin² A + Cos² A = 1
=> Sin² 30° + Cos² 30°
=>1
Answer:-
The value of the expression :
Sin 750° Cos 300° + Cos 1470° Sin (-1020°) is 1
Used formulae:-
- Sin (360°+A) = Sin A
- Cos (360°+A) = Cos A
- Sin (-A) = - Sin A
- Cos (270°+A) = Sin A
- Sin (360°-A) = - Sin A
- Sin 30° = 1/2
- Cos 60° = √3/2
- Cos 30° = √3/2
- Sin (90°-A) = Cos A
- Sin² A + Cos² A = 1
Step-by-step explanation:
please check the values may be the values are wrong . if any query then ask
