79.6k views
5 votes
Solve the equation: tan^2x+cot^2x=2​

Solve the equation: tan^2x+cot^2x=2​-example-1
User Mironych
by
7.2k points

2 Answers

1 vote

Answer:

45 degrees

Explanation:

Convert both tan and cot to sin and cos:

Let theta = x (because I can't put theta here)


tan^(2) x + cot^(2)x = 2\\(sin^(2) )/(cos^(2) ) + (cos^(2) )/(sin^(2) ) =2\\(sin^(4)x + cos^(4)x )/(cos^(2)xsin^(2)x  )  =2 \\sin^(4)x + cos^(4)x = 2cos^(2)xsin^(2)x\\sin^(4)x + cos^(4)x - 2cos^(2)xsin^(2)x =0 \\sin^(4)x  - 2cos^(2)xsin^(2)x + cos^(4)x = 0\\(sin^(2)x - cos^(2)x)^(2)  =0\\sin^(2)x - cos^(2)x =0\\sin^(2)x = cos^(2)x \\(sin^(2)x)/(cos^(2)x)  = 1\\tan^(2)x = 1\\x = 45 degrees

User YAMAMOTO Yusuke
by
7.9k points
5 votes

Good evening ,

___________________

Explanation:

Look at the photo below for the detailed answer.

:)

Solve the equation: tan^2x+cot^2x=2​-example-1
User Perkss
by
8.4k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories