Question

please help me to solve this question.​

Answer 1

$\theta \: and \: \phi \: are \: complementary$

$\theta + \phi = 90{}^{o} \\</p><p>\phi = 90{}^{o} - \theta$ ... (i)

$cosec \theta sec \phi - cot \theta tan \phi \\</p><p>= cosec \theta sec(90{}^{o} - \theta) - cot \theta tan(90{}^{o} - \theta$ ... (from i)

$</p><p>= cosec \theta cosec \theta - cot \theta cot \theta$ ... sec(90° - A) = cosecA

... tan(90° - A) = cotA

$</p><p>= cosec{}^{2} \theta - cot{}^{2} \theta \\</p><p>= 1$ ... (1 + cot²A = cosec²A)

Hence,

$cosec \theta sec \phi - cot \theta tan \phi = 1$