Question

Solve the equation: tan^2x+cot^2x=2​

Answer 1

Answer:

45 degrees

Step-by-step explanation:

Convert both tan and cot to sin and cos:

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

$tan^{2} x + cot^{2}x = 2\\\frac{sin^{2} }{cos^{2} } + \frac{cos^{2} }{sin^{2} } =2\\\frac{sin^{4}x + cos^{4}x }{cos^{2}xsin^{2}x } =2 \\sin^{4}x + cos^{4}x = 2cos^{2}xsin^{2}x\\sin^{4}x + cos^{4}x - 2cos^{2}xsin^{2}x =0 \\sin^{4}x - 2cos^{2}xsin^{2}x + cos^{4}x = 0\\(sin^{2}x - cos^{2}x)^{2} =0\\sin^{2}x - cos^{2}x =0\\sin^{2}x = cos^{2}x \\\frac{sin^{2}x}{cos^{2}x} = 1\\tan^{2}x = 1\\x = 45 degrees$

Answer 2

Good evening ,

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Step-by-step explanation:

Look at the photo below for the detailed answer.

:)