Question

Prove that (cosecø-sinø)(secø-cosø)(tanø+cotø)=1

Answer 1

I hope this helps you.

I am happy to help you with this question.

Pls mark it as brainliest.

Answer 2

Prove that:

$(cosec\theta - sin\theta)(sec\theta - cos\theta)(tan\theta + cot\theta) = 1.$

Proof:

L.H.S:

$= (cosec\theta - sin\theta)(sec\theta - cos\theta)(tan\theta + cot\theta)\\\\= (\frac{1}{sin\theta} - sin\theta)(\frac{1}{cos\theta}-cos\theta )(\frac{sin\theta}{cos\theta}+\frac{cos\theta}{sin\theta})\\\\= (\frac{1-sin^{2}\theta }{sin\theta})(\frac{1-cos^{2}\theta}{cos\theta})(\frac{sin^{2}\theta+cos^{2}\theta}{sin\theta.cos\theta})\\\\= (\frac{cos^{2}\theta}{sin\theta})(\frac{sin^{2}\theta}{cos\theta})(\frac{1}{sin\theta.cos\theta})\\\\= \frac{cos\theta.sin\theta}{cos\theta.sin\theta} = 1.$

Trigonometric Formulas and Identities used:

$1. \: cosec\theta = \frac{1}{sin\theta}\\\\2. \: sec\theta = \frac{1}{cos\theta}\\\\3. \: tan\theta = \frac{sin\theta}{cos\theta}\\\\4. \: cot\theta = \frac{cos\theta}{sin\theta}\\\\5. \: sin^{2}\theta + cos^{2}\theta = 1$