Question

If $\theta$ is an acute angle, find the denominator A, when $(cosec\theta-cot\theta)^2=\frac{1-cot\theta}{A}$

• A. $$cosec\theta-1$$
• B. $$1+sin\theta$$
• C. $$cot\theta$$
• D. $$1+cos\theta$$

Answer 1

Answer:

$$1+cos\theta$$

$(cosec\theta-cot\theta)^2=\frac{1-cos\theta}{A}$

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

$=(\frac{1-cos\theta}{sin\theta})^2$

$=\frac{(1-cos\theta)^2}{sin^2\theta}$

$=\frac{(1-cos\theta)^2}{(1-cos^2\theta)}$

$=\frac{(1-cos\theta)(1-cos\theta)}{((1-cos\theta)(1+cos\theta)}$

$=\frac{(1-cos\theta)}{(1+cos\theta)}$

which is equal to $\frac{(1-cos\theta)}{A}$