If sin A=\(\frac { 3 }{ 5 } \), 0\(\frac { \pi }{ 2 } \) and cos B=\(-\frac { 12 }{ 13 } \), \(\pi \) \(\frac { 3\pi }{ 2 } \) , then find the following.
sin (A - B)

If sin A=\(\frac { 3 }{ 5 } \), 0\(\frac { \pi }{ 2 } \) and cos B=\(-\frac { 12 }{ 13 } \), \(\pi \) \(\frac { 3\pi }{ 2 } \) , then find the following.
cos (A + B)

Solve sin2x-sin4x+sin6x=0

The Moon's distance from the Earth is 360000 km and its diameter subtend an angle of 31' at the eye of observer. Find the diameter of the Moon.

Two trees A and B are on the same side of a river. From a point C in the river the distance of trees A and B are 250m and 300m, respectively of the angle C is 45⁰, find the distance between the trees.[use \(\sqrt { 2 } =1.44\)]

Find the values of other five trigonometric functions cot x = \(3\over4\) ,x lies in third quadrant.

Prove the following:
\({sin 5x + sin 3x \over cos 5x + cos 3x }=tan 4x\)

Find the general solution for each of the following equations
sin 2x + cos x = 0

Prove that,
2cos\({\pi\over13}\)cos\({9\pi\over13}\)+cos\({3\pi\over13}\)+cos\({5\pi\over13}\)=0

In any ∆ABC, prove that: \(a\quad sin\frac { A }{ 2 } sin\frac { B-C }{ 2 } +b\quad sin\frac { B }{ 2 } sin\frac { C-A }{ 2 } +c\quad sin\frac { C }{ 2 } sin\left( \frac { A-B }{ 2 } \right) =0\)

Prove that: \({cos 6\theta +6cos 4\theta+15cos 2\theta+10\over cos5\theta+5cos 3\theta+10cos\theta}=2cos \theta\)