Question

sin 70°cos 10°-cos 70°sin 10=√3/2

Answer 1

Let a =70° and b= 10° (and a-b=70-10 =60)
We have the following trigonometric identity:

sin(a-b) = sin(a).cos(b)-sin(b).cos(a) OR:
sin(70-10) = sin70.cos10 - sin10.cos70
But sin(70-10) = sin(60) and we know that sin(60°) =(√3)/2

Answer 2

The value of sin 70°cos 10°-cos 70°sin 10=√3/2

What is the value of sin(a-b)?

sin(a-b) can be calculated by the formula given below

sin(a-b)=sina.cosb - cosa.sinb

where a and b are the measure of the angles

here it is given that

sin 70°cos 10°-cos 70°sin 10

For applying the formula for sin(a-b)

here a=70°

and b=10°

As sina.cosb - cosa.sin =sin(a-b)

sin 70°cos 10°-cos 70°sin 10

=sin(70°-10°)

=sin 60°

=√3/2

Therefore the value of sin 70°cos 10°-cos 70°sin 10=√3/2

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