Solve cos - 1 cos - 1 -32 - -6

We have, #10; #10; cos( cos^ 1( √(3)2 #10;)+π6) #10; #10; =cos( cos^ 1( cosπ6 #10;)+π6) #10; #10; =cos( π6+π6) #10; #10; ...

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Byju's Answer

Standard XII

Mathematics

Trigonometric Ratios of Compound Angles

Solve cos -...

Question

Solve ${cos}^{- 1} ({cos}^{- 1} (\frac{\sqrt{3}}{2}) + \frac{π}{6})$

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Solution

We have,

$cos ({cos}^{- 1} (\frac{\sqrt{3}}{2}) + \frac{π}{6})$

$= cos ({cos}^{- 1} (cos \frac{π}{6}) + \frac{π}{6})$

$= cos (\frac{π}{6} + \frac{π}{6})$

$= cos (\frac{π}{3})$

$= \frac{1}{2}$

Hence, this is the answer.

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Solve cos−1(cos−1(√32)+π6)

We have, cos(cos−1(√32)+π6) =cos(cos−1(cosπ6)+π6) =cos(π6+π6) =cos(π3) =12 Hence, this is the answer.

Solve ${cos}^{- 1} ({cos}^{- 1} (\frac{\sqrt{3}}{2}) + \frac{π}{6})$

We have,

$cos ({cos}^{- 1} (\frac{\sqrt{3}}{2}) + \frac{π}{6})$

$= cos ({cos}^{- 1} (cos \frac{π}{6}) + \frac{π}{6})$

$= cos (\frac{π}{6} + \frac{π}{6})$

$= cos (\frac{π}{3})$

$= \frac{1}{2}$

Hence, this is the answer.