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Harlamova29_29 [7]
2 years ago
12

Use trigonometric identities to simplify each expression. 1/cot^2 (x) - 1/cos^2(x)

Mathematics
1 answer:
PtichkaEL [24]2 years ago
7 0

Answer:

- 1

Step-by-step explanation:

\frac{1}{\cot ^2\left(x\right)}-\frac{1}{\cos ^2\left(x\right)}\\\\\mathrm{Use\:the\:basic\:trigonometric\:identity}:\quad \frac{1}{\cos \left(x\right)}=\sec \left(x\right),\\\frac{1}{\cot ^2\left(x\right)}-\sec ^2\left(x\right)\\\\\mathrm{Use\:the\:basic\:trigonometric\:identity}:\quad \frac{1}{\cot \left(x\right)}=\tan \left(x\right),\\\tan ^2\left(x\right)-\sec ^2\left(x\right)\\\\=> \frac{\sin ^2\left(x\right)}{\cos ^2\left(x\right)}-\frac{1}{\cos ^2\left(x\right)}\\

=> \frac{\sin ^2\left(x\right)-1}{\cos ^2\left(x\right)}\\\\=> -\frac{\cos ^2\left(x\right)}{\cos ^2\left(x\right)}\\=> - 1

Hope  that  helps!

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