Why are the magnification properties of microscopes and telescopes defined in terms of the ratio of angles and not in terms of the ratio of sizes of objects and images?

Express the ratios cos A, tan A and sec A in terms of sin A.

Write all the other trigonometric ratios of angleA in terms of sec A .

Express all the other trigonometric ratios of angleA in terms of sin A.

Express cot 85° + cos 75° in terms of trigonometric ratios of angles between 0 ° and 45°

Express sin 67° + cos 75° in terms of trigonometric ratios of angles between 0° and 45°

Express the trigonometric ratios sinA, sec A and tan A in terms of cot A.

Express cos 63° + cot 59° - sec 47° in terms of trigonometric ratios of angles between 0° and 45° .

If the arithmetic progression whose common difference is nonzero the sum of first 3n terms is equal to the sum of next n terms. Then, find the ratio of the sum of the 2n terms to the sum of next 2n terms.

(a) A giant refracting telescope at an observatory has an objective lens of focal length 15m. If an eyepiece of focal length 1.0cm is used, what is the angular magnification of the telescope? (b) If this telescope is used to view the moon, what is the diameter of the image of the moon formed by the objective lens? The diameter of the moon is 3.48 xx 10^(6)m , and the radius of lunar orbit is 3.8xx10^(8)m .