19, coS COSs equal tocos-is equal toTrC) 3D)

Open in App

Solution

The given function is cos −1 ( cos 7π 6 ).

It is known that cos −1 ( cosx )=x, if x∈[ 0,π ]. But 7π 6 ∉[ 0,π ]. So,

cos −1 ( cos 7π 6 )= cos −1 ( cos( − 7π 6 ) ) = cos −1 ( cos( 2π− 7π 6 ) ) = cos −1 ( cos( 5π 6 ) )

Now, 5π 6 ∈[ 0,π ]. So,

cos −1 ( cos 7π 6 )= cos −1 ( cos 5π 6 ) = 5π 6

Thus, the value of cos −1 ( cos 7π 6 )is 5π 6 .

Therefore, option (B) is correct.

Suggest Corrections

Similar questions

y = {cos}^{- 1} (\frac{9 - x^{2}}{9 + x^{2}})

y^{'} (- 1)

A + B + C = 2 S

cos (S - A) + cos (S - B) + cos (S - C) + cos S = 4 cos \frac{A}{2} cos \frac{B}{2} cos \frac{C}{2}

x = c o sec ({tan}^{- 1} (cos ({cot}^{- 1} (sec ({sin}^{- 1} a))))); y = sec ({cot}^{- 1} (sin ({tan}^{- 1} (c o sec ({cos}^{- 1} a)))))

a \in [0, 1]

Prove that:

cos x coss 2x cos 4x cos 8x = sin 16x/ 16sin x

\frac{sin 19^{\circ}}{cos 71^{\circ}} + \frac{cos 73^{\circ}}{sin 17^{\circ}}

Join BYJU'S Learning Program