What is the least value of $$25\cos e{c^2}x + 36{\sec ^2}x$$ ?

What is the value of $${{\sin 34^\circ \cos 236^\circ - \sin 56^\circ \sin 124^\circ } \over {\cos 28^\circ \cos 88^\circ + \cos 178^\circ \sin 208^\circ }}$$ ?

tan54$$^\circ$$ can be expressed as

Read the given information carefully and answer the given questions.

If $$p = X\cos \theta - Y\sin \theta $$,

$$q = X\sin \theta + Y\cos \theta $$ and

$${p^2} + 4pq + {q^2} = A{X^2} + B{Y^2}$$, $$0 \le \theta \le {\pi \over 2}$$.

What is the value of $$\theta$$ ?