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Solve the equation $x\tan\left(\theta\right)^2-\sin\left(a\right)^2=\tan\left(a\right)^2\sin\left(a\right)^2$

Step-by-step Solution

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Solution

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Final answer to the problem

$\theta=\arctan\left(\sqrt{\frac{\sin\left(a\right)^2\left(\tan\left(a\right)^2+1\right)}{x}}\right),\:\theta=\arctan\left(-\sqrt{\frac{\sin\left(a\right)^2\left(\tan\left(a\right)^2+1\right)}{x}}\right)$
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Step-by-step Solution

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We need to isolate the dependent variable , we can do that by simultaneously subtracting $-\sin\left(a\right)^2$ from both sides of the equation

$x\tan\left(\theta\right)^2=\tan\left(a\right)^2\sin\left(a\right)^2-\left(-1\right)\sin\left(a\right)^2$

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$x\tan\left(\theta\right)^2=\tan\left(a\right)^2\sin\left(a\right)^2-\left(-1\right)\sin\left(a\right)^2$

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Learn how to solve trigonometric equations problems step by step online. Solve the equation xtan(t)^2-sin(a)^2=tan(a)^2sin(a)^2. We need to isolate the dependent variable , we can do that by simultaneously subtracting -\sin\left(a\right)^2 from both sides of the equation. Multiply -1 times -1. Factor the polynomial \tan\left(a\right)^2\sin\left(a\right)^2+\sin\left(a\right)^2 by it's greatest common factor (GCF): \sin\left(a\right)^2. Divide both sides of the equation by x.

Final answer to the problem

$\theta=\arctan\left(\sqrt{\frac{\sin\left(a\right)^2\left(\tan\left(a\right)^2+1\right)}{x}}\right),\:\theta=\arctan\left(-\sqrt{\frac{\sin\left(a\right)^2\left(\tan\left(a\right)^2+1\right)}{x}}\right)$

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Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

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Function Plot

Plotting: $x\tan\left(t\right)^2-\sin\left(a\right)^2-\tan\left(a\right)^2\sin\left(a\right)^2$

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x
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(◻)
+
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×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

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Main Topic: Trigonometric Equations

A trigonometric equation is an equation in which one or more trigonometric ratios appear.

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