Simplifying cot(15°) - tan(15°)
To find the value of the expression $\cot(15^\circ) - \tan(15^\circ)$, we can use a known trigonometric identity.
Using Trigonometric Identities
Recall the identity:
$ \cot(x) - \tan(x) = 2 \cot(2x) $Substitute $x = 15^\circ$ into the identity:
$ \cot(15^\circ) - \tan(15^\circ) = 2 \cot(2 \times 15^\circ) $ $ = 2 \cot(30^\circ) $Calculating the Final Value
We know the value of $\cot(30^\circ)$ is $\sqrt{3}$.
Therefore, the expression evaluates to:
$ 2 \times \sqrt{3} = 2\sqrt{3} $The value of $\cot(15^\circ) - \tan(15^\circ)$ is $2\sqrt{3}$.
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:
