CameraIcon

SearchIcon

MyQuestionIcon

1

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

Sum of Trigonometric Ratios in Terms of Their Product

The value of ...

Question

The value of ${(sin \frac{π}{8} + i cos \frac{π}{8})}^{8}$

A

-1

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

B

1

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

C

0

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

D

None of these

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

Open in App

Solution

The correct option is A -1
$z = {(sin \frac{π}{8} + i cos \frac{π}{8})}^{8} = [i (cos \frac{π}{8} - i sin \frac{π}{8})]]^{8}$
...{ $∵ i^{8} = 1$ }
$\Rightarrow z = cos π - i sin π = - 1$ ...{De Moivre's Theorem}
Hence, option 'A' is correct.

Suggest Corrections

thumbs-up

0

Similar questions

Q. The value of

(s i n \frac{π}{8} + i cos \frac{π}{8})^{8} (s i n \frac{π}{8} - i c o s \frac{π}{8})^{8}

{⎛ ⎜ ⎜ ⎝ \frac{sin \frac{π}{8} + i cos \frac{π}{8}}{sin \frac{π}{8} - i cos \frac{π}{8}} ⎞ ⎟ ⎟ ⎠}^{8}

\frac{{(sin π / 8 + i cos π / 8)}^{8}}{{(sin π / 8 - i cos π / 8)}^{8}}

Q. Show that one value of

{⎛ ⎜ ⎜ ⎝ \frac{1 + sin \frac{π}{8} + i cos \frac{π}{8}}{1 + sin \frac{π}{8} - i cos \frac{π}{8}} ⎞ ⎟ ⎟ ⎠}^{\frac{8}{3}}

- 1

Q. The expression

{⎡ ⎢ ⎢ ⎣ \frac{1 + sin \frac{π}{8} + i cos \frac{π}{8}}{1 + sin \frac{π}{8} - i cos \frac{π}{8}} ⎤ ⎥ ⎥ ⎦}^{8} =

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Transformations

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Sum of Trigonometric Ratios in Terms of Their Product

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon