Question

show that tan theta + cot theta is equal to co secant theta into secant theta ​

Answer 1

To prove:

cot \theta +tan \theta =cosec \theta \times sec \theta

Answer:

cot\theta + tan\theta = cosec \theta \times sec \theta

LHS is

Cot \theta + tan \theta= \frac {cos \theta }{sin \theta }+ \frac {sin \theta }{ cos \theta }

= \frac {cos^{2} \theta + sin^{2} \theta}{ sin \theta \times cos \theta}

Therefore cos^{2} \theta + sin^{2} \theta = 1

= \frac {1}{ sin \theta \times cos \theta}

= \frac {1}{ sin \theta} \times \frac {1}{ cos \theta}

Therefore,

cot \theta +tan \theta =cosec \theta \times sec \theta

Hence proved.