Question

Find the value if 4(sec square 59-cot square 31)/3

Answer 1

Answer:

$Value \: of \:\frac{4(sec^{2}59-cot^{2}31)}{3}=\frac{4}{3}$

Step-by-step explanation:

$Value \: of \:\frac{4(sec^{2}59-cot^{2}31)}{3}$

$=\frac{4(sec^{2}59-cot^{2}(90-59)}{3}$

$=\frac{4(sec^{2}59-cot^{2}(90-59)}{3}$

$=\frac{4(sec^{2}59-tan^{2}59)}{3}$

$= \frac{4\times 1}{3}$

/* By trigonometric identity:

sec²A - tan²A = 1 */

$=\frac{4}{3}$

Therefore,

$Value \: of \:\frac{4(sec^{2}59-cot^{2}31)}{3}=\frac{4}{3}$

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