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4 years ago

Solve the equation: tan^2x+cot^2x=2

Mathematics

2 answers:

andrew11 [14]4 years ago

6 0

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)

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

garri49 [273]4 years ago

4 0

Good evening ,

___________________

Step-by-step explanation:

Look at the photo below for the detailed answer.

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3 years ago

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Lets solve our radical equation $\sqrt{x+6}-4=x$ step by step.

Step 1 add 4 to both sides of the equation:

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Step 2 square both sides of the equation:

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Step 3 expand the binomial in the right hand side:

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Step 5 factor the expression:

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Step 6 solve for each factor:

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The solution $x=2$ is a valid solution of the rational equation $\sqrt{x+6}-4=x$ .

For $x=-5$

$\sqrt{x+6}-4=x$

$\sqrt{-5+6}-4=-5$

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Since -3 is not equal to -5, the solution $x=-5$ is not a valid solution of the rational equation $\sqrt{x+6}-4=x$ ; therefore, $x=-5$ is an extraneous solution of the equation.

We can conclude that even all the algebraic procedures of Israel are correct, he did not check for extraneous solutions.

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3 years ago

Solve the equation: tan^2x+cot^2x=2​

Solve the equation: tan^2x+cot^2x=2