PDF chapter test TRY NOW

1. (i) If \(\frac{cos \ \alpha}{cos \ \beta} = m\) and \(\frac{cos \ \alpha}{sin \ \beta} = n\), then prove that \((m^2 + n^2) cos^2 \ \beta = n^2\).
 
(ii) If \(\cot \theta + \tan \theta = x\) and \(\sec \theta - \cos \theta = y\), then prove that \((x^2 y)^{\frac{2}{3}} - (x y^2)^{\frac{2}{3}} = 1\).
 
2. (i) If \(sin \ \theta + cos \ \theta = p\) and \(sec \ \theta + cosec \ \theta = q\), then prove that \(q(p^2 - 1) = 2p\)
 
(ii) If \(sin \ \theta(1 + sin^2 \ \theta) = cos^2 \ \theta\), then prove that \(cos^6 \ \theta - 4 cos^4 \ \theta + 8 cos^2 \ \theta = 4\).
 
3. If \(\frac{\cos \theta}{1 + \sin \theta} = \frac{1}{a}\), then prove that \(\frac{a^2 - 1}{a^2 + 1} = \sin \theta\).
 
Important!
This is a self-assessment task. Solve this question and assess the solution steps after completing the test on your own.