Question

Prove Tan^2 theta + cot^2 theta +2 = cosec^2 theta × sec^2 theta

Answer 1

Step-by-step explanation:

$tan^{2} \alpha + cot^{2}\alpha +2= (tan\alpha +cot\alpha)^{2}\\</p><p>=> (\frac{sin\alpha}{cos\alpha} + \frac{cos\alpha}{sin\alpha})^2\\</p><p>=>(\frac{sin^2\alpha+cos^2\alpha}{sin\alpha cos\alpha})^2\\</p><p>=>(\frac{1}{sin\alpha cos\alpha})^2\\</p><p>=> (cosec\alpha sec\alpha)^2\\</p><p>=> cosec^2\alpha *sec^2\alpha\\</p><p>=>RHS$