Cos 3- 4 -x -cos 3- 4 -x - 2 -sin x

The correct option is A TrueAs we know that cos (A+B) cos(A B)= 2sin Asin B cos(3π4+x) cos(3π4 x)= 2sin3π4sin x=2√(2)sin x=√(2)sin x So the relation i ...

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Byju's Answer

Standard XII

Mathematics

Trigonometric Ratios of Multiples of an Angle

cos 3π 4 +x ...

Question

$cos (\frac{3 π}{4} + x) - cos (\frac{3 π}{4} - x) = \sqrt{2} . sin x$

True

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False

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Solution

The correct option is A True
As we know that
$cos (A + B) - cos (A - B) = - 2 sin A sin B$
$cos (\frac{3 π}{4} + x) - cos (\frac{3 π}{4} - x) = - 2 sin \frac{3 π}{4} sin x = \frac{2}{\sqrt{2}} sin x = \sqrt{2} sin x$
So the relation is $True$

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Similar questions

Q. Prove that:

cos (\frac{3 π}{4} + x) - cos (\frac{3 π}{4} - x) = - \sqrt{2} sin x

Q. If

cos (\frac{3 π}{4} + x) - cos (\frac{3 π}{4} - x) = - \sqrt{m} sin x

.Find

m

Q. Prove the following:

c o s (\frac{3 π}{4} + x) - c o s (\frac{3 π}{4} - x) = - \sqrt{2} s i n x

Q. Find

(cos (\frac{π}{4} + x) + cos (\frac{π}{4} - x) - \sqrt{2} cos x)

(cos (\frac{3 π}{4} + x) - cos (\frac{3 π}{4} - x) + \sqrt{2} sin x)

Prove that

$(i) cos (\frac{π}{4} + x) + cos (\frac{π}{4} - x) = \sqrt{2} cos x$

(ii) $cos (\frac{3 π}{4} + x) - cos (\frac{3 π}{4} - x) = - \sqrt{2} sin x$

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cos(3π4+x)−cos(3π4−x)=√2.sinx

The correct option is A TrueAs we know thatcos(A+B)−cos(A−B)=−2sinAsinBcos(3π4+x)−cos(3π4−x)=−2sin3π4sinx=2√2sinx=√2sinxSo the relation is True

$cos (\frac{3 π}{4} + x) - cos (\frac{3 π}{4} - x) = \sqrt{2} . sin x$

The correct option is A True
As we know that
$cos (A + B) - cos (A - B) = - 2 sin A sin B$
$cos (\frac{3 π}{4} + x) - cos (\frac{3 π}{4} - x) = - 2 sin \frac{3 π}{4} sin x = \frac{2}{\sqrt{2}} sin x = \sqrt{2} sin x$
So the relation is $True$