Show that \(\frac { (cos\theta -cos3\theta )(sin8\theta +sin2\theta ) }{ (sin5\theta -sin\theta )(cos4\theta -cos6\theta ) } =1\)

If \(\sin { x } =\frac { 15 }{ 17 } \) and \(\cos {y } =\frac { 12 }{ 13 } \), 0 < x < \(\frac{\pi}{2}\), 0 < y < \(\frac{\pi}{2}\), find the value of sin (x + y)

Find cos(x - y), given that cos x = \(-\frac{4}{5}\) with \(\pi<x<{{3\pi}\over{2}}\) and \(sin \ y = -{{24}\over{25}}\) with \(\pi<x<{{3\pi}\over{2}}\). 

For each given Angle, find a coterminal angle with a measure of \(\theta\) such that \(0^o\le \theta \le 360°\) 
395⁰ 

Prove that \(sinx+sin2x+sin3x=sin2x(1+2cosx)\)

Prove that \(\frac { sin4x+sin2x }{ cos4x+cos2x } =tan3x\)

If a cos \(\theta\) - b sin \(\theta\) = c, show that a sin \(\theta\) + b cos \(\theta\) = \(\pm \sqrt { { a }^{ 2 }+{ b }^{ 2 }-{ c }^{ 2 } } \)

If sin \(\theta\) + cos \(\theta\) = m, show that cos⁶\(\theta\) + sin⁶\(\theta\)  = \(\frac { 4-3({ m }^{ 2 }-1)^{ 2 } }{ 4 } \), where m² \(\le \) 2

What must be the radius of a circular running path, around which an athlete must run 5 times in order to describe 1 km?

If in two Circles, arcs of the same length subtend angles 60⁰ and 75⁰ at the center, find the ratio of their radii