Question

If 13 sino - coso = 0 and 0° <o < 90°, then the value of 0 is
(a) 30° (b) 60° (c) 45° (d) none of these​

Answer 1

The value of the angle is (d)none of these.

• Given condition is : 13sinФ - cosФ = 0
• Now we re-arrange this terms as:

13sinФ = cosФ   (given condition)

• We know the identity as :

sin²Ф + cos²Ф = 1

• Substituting the given condition in the identity we get

sin²Ф + (13sin²Ф) = 1

sin²Ф + 169sin² = 1

170sin²Ф = 1

sin²Ф = $\frac{1}{170}$

sinФ = √$\frac{1}{170}$

Ф = $sin^{-1}$(√$\frac{1}{170}$)

Ф = 4.398°