PUC Science Class 11 - Karnataka Board PUC Question Bank Solutions for Mathematics

Write the value of sin \[\frac{\pi}{12}\] sin \[\frac{5\pi}{12}\].

If sin A + sin B = α and cos A + cos B = β, then write the value of tan \[\left( \frac{A + B}{2} \right)\].

If cos A = m cos B, then write the value of \[\cot\frac{A + B}{2} \cot\frac{A - B}{2}\].

Write the value of the expression \[\frac{1 - 4 \sin 10^\circ \sin 70^\circ}{2 \sin 10^\circ}\]

If A + B = \[\frac{\pi}{3}\] and cos A + cos B = 1, then find the value of cos \[\frac{A - B}{2}\].

Write the value of \[\sin\frac{\pi}{15}\sin\frac{4\pi}{15}\sin\frac{3\pi}{10}\]

If sin 2A = λ sin 2B, then write the value of \[\frac{\lambda + 1}{\lambda - 1}\]

Write the value of \[\frac{\sin A + \sin 3A}{\cos A + \cos 3A}\]

cos 40° + cos 80° + cos 160° + cos 240° =

sin 163° cos 347° + sin 73° sin 167° =

If sin 2 θ + sin 2 ϕ = \[\frac{1}{2}\] and cos 2 θ + cos 2 ϕ = \[\frac{3}{2}\], then cos² (θ − ϕ) =

The value of cos 52° + cos 68° + cos 172° is

The value of sin 78° − sin 66° − sin 42° + sin 60° is ______.

If sin α + sin β = a and cos α − cos β = b, then tan \[\frac{\alpha - \beta}{2}\]=

cos 35° + cos 85° + cos 155° =

The value of sin 50° − sin 70° + sin 10° is equal to

sin 47° + sin 61° − sin 11° − sin 25° is equal to

If cos A = m cos B, then \[\cot\frac{A + B}{2} \cot\frac{B - A}{2}\]=

If A, B, C are in A.P., then \[\frac{\sin A - \sin C}{\cos C - \cos A}\]=