A fighter jet has to hit a small target by flying a horizontal distance. When the target is sighted, the pilot measures the angle of depression to be 30⁰. If after 100 km, the target has an angle of depression of 60⁰, how far is the target from the fighter jet at that instant?

A man starts his morning walk at a point A reaches two points B and C and finally back to A such that ㄥA = 60⁰ and ㄥB = 45⁰, AC = 4 km in ΔABC. Find the total distance he covered during his morning walk.

If \(\frac { cos^{ 4 }\alpha }{ { cos }^{ 2 }\beta } +\frac { { sin }^{ 4 }\alpha }{ { sin }^{ 2 }\beta } =1\) prove that \(\frac { { cos }^{ 4 }\beta }{ { cos }^{ 2 }\alpha } +\frac { { sin }^{ 4 }\beta }{ { sin }^{ 2 }\alpha } =1\)

If sec \(\theta\) + tan \(\theta\) = p, obtain the values of sec \(\theta\), tan \(\theta\) and sin \(\theta\) in terms of p

Eliminate \(\theta\) from the equation a sec \(\theta\) - c tan \(\theta\) = b and b sec \(\theta\)  + d tan \(\theta\) = C

Show that \(cot(A+{ 15 }^{ 0 })-tan(A-{ 15 }^{ 0 })=\frac { 4cos2A }{ 1+2sin2A } \)

If A + B + C = 180⁰, prove that \(cosA+cosB-cosC=-1+4cos\frac { A }{ 2 } cos\frac { B }{ 2 } sin\frac { C }{ 2 } \)

If x cos \(\theta\) = y cos \(\left( \theta +\frac { 2\pi }{ 3 } \right) \) = z cos \(\left( \theta +\frac { 4\pi }{ 3 } \right) \), find the value of xy + yz + zx.

If A + B + C = 180⁰, prove that \(sinA+sinB+sinC=4cos\frac { A }{ 2 } cos\frac { B }{ 2 } cos\frac { C }{ 2 } \)

If x + y + z = xyz, then prove that \(\frac { 2x }{ 1-{ x }^{ 2 } } +\frac { 2y }{ 1-{ y }^{ 2 } } +\frac { 2z }{ 1-{ z }^{ 2 } } =\frac { 2x }{ 1-{ x }^{ 2 } } \frac { 2y }{ 1-{ y }^{ 2 } } \frac { 2z }{ 1-{ z }^{ 2 } } \)