NCERT Exemplar Solutions
Class 11 - Mathematics - Chapter 3: TRIGONOMETRIC FUNCTIONS

Fill in the blanks in Exercises 60 to 67 :

The value of \( \dfrac{\sin 50^\circ}{\sin 130^\circ} \) is ____.

If \( k = \sin\left(\dfrac{\pi}{18}\right) \sin\left(\dfrac{5\pi}{18}\right) \sin\left(\dfrac{7\pi}{18}\right) \), then the numerical value of \( k \) is ____.

If \( \tan A = \dfrac{1 - \cos B}{\sin B} \), then \( \tan 2A = ____ \).

If \(\sin x + \cos x = a\), then

(i) \( \sin^6 x + \cos^6 x = ____ \)

(ii) \(|\sin x - \cos x| = ____ \)

In a triangle ABC with \(\angle C = 90^\circ\) the equation whose roots are \(\tan A\) and \(\tan B\) is ____.

\(3(\sin x - \cos x)^4 + 6(\sin x + \cos x)^2 + 4(\sin^6 x + \cos^6 x) = ____\).

Given \(x > 0\), the values of \( f(x) = -3 \cos \sqrt{3 + x + x^2} \) lie in the interval ____.

The maximum distance of a point on the graph of the function \( y = \sqrt{3} \sin x + \cos x \) from x-axis is ____.