Solving Trigonometric Equation
The problem asks for the value of x in degrees, given the equation:
$ \sqrt{2} \sin(5x - 5)^\circ = \tan 45^\circ $
Equation Steps
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Evaluate Known Tangent Value: We know that $\tan 45^\circ = 1$. Substituting this into the equation gives:
$ \sqrt{2} \sin(5x - 5)^\circ = 1 $
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Isolate the Sine Function: Divide both sides by $\sqrt{2}$:
$ \sin(5x - 5)^\circ = \frac{1}{\sqrt{2}} $
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Identify the Angle for Sine: Recall that $\sin 45^\circ = \frac{1}{\sqrt{2}}$. Therefore, we can equate the angles:
$ (5x - 5)^\circ = 45^\circ $
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Solve for 5x: Add 5 to both sides of the equation:
$ 5x^\circ = 45^\circ + 5^\circ $
$ 5x^\circ = 50^\circ $
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Solve for x: Divide both sides by 5:
$ x = \frac{50^\circ}{5} $
$ x = 10 $
The value of x is 10 degrees.
Similar Questions
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Important Questions from Trigonometric Ratios and Identities
What is the ratio of the greatest to the smallest value of 2 – 2 sin x – sin 2x, 0 ≤ x ≤ (π/2)?
If sinθ = \(\frac{4}{5}\) , Find the value of sin3θ
If x, y are acute angles, where 0 < x + y < 90° and sin(3x - 40°) = cos (3y + 40°), then the value of tan (x + y) is equal to
What is (1 + cot θ - cosec θ)(1 + tan θ + sec θ) equal to?
If \(\sin \theta =\frac{3}{5}\) and \(\cos \theta =\frac{4}{5}\) , then the value of \(\frac{1+\tan \theta}{1-\cot \theta}\) is:
