化简-(101)/(cos^2(a))+(101)/(cot^2(a))

解答

化简

- \frac{101}{cos ^{2} ( a )} + \frac{101}{cot ^{2} ( a )}

- 101

求解步骤

- \frac{101}{cos ^{2} ( a )} + \frac{101}{cot ^{2} ( a )}

使用基本三角恒等式:

\frac{1}{cos ( x )} = sec (x)

= \frac{101}{cot ^{2} ( a )} - 101 sec^{2} (a)

使用基本三角恒等式:

\frac{1}{cot ( x )} = tan (x)

= 101 tan^{2} (a) - 101 sec^{2} (a)

使用毕达哥拉斯恒等式:

sec^{2} (x) = tan^{2} (x) + 1

sec^{2} (x) - tan^{2} (x) = 1

= 101 (- 1)

因式分解出通项

101

= 101 (tan^{2} (a) - sec^{2} (a))

= - 101

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