Cos - 4 -x -cos - 4 -x - 2 -cos x

The correct option is B FalseAs we know that cos (A+B)+cos(A B)=2cos Acos B cos(π4+x)+cos(π4 x)=2cosπ4cos x=2√(2)cos x=√(2)cos x So the relation is ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Trigonometric Ratios of Compound Angles

cos π 4 +x +...

Question

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

True

No worries! We‘ve got your back. Try BYJU‘S free classes today!

False

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

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

Suggest Corrections

Similar questions

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

Q. Prove that

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

Q. The range of the function

f (x) = {log}_{\sqrt{5}} (3 + cos (\frac{3 π}{4} + x) + cos (\frac{π}{4} + x) + cos (\frac{π}{4} - x) - cos (\frac{3 π}{4} - x))

Join BYJU'S Learning Program

cos(π4+x)+cos(π4−x)=−√2.cosx

The correct option is B FalseAs we know thatcos(A+B)+cos(A−B)=2cosAcosBcos(π4+x)+cos(π4−x)=2cosπ4cosx=2√2cosx=√2cosxSo the relation is False

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

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