Problem Analysis:
- We are given the value of $\tan A = \frac{3}{4}$.
- We need to find the value of the expression $\frac{\cos A - \sin A}{\cos A + \sin A}$.
Trigonometric Expression Calculation
A straightforward method is to divide both the numerator and the denominator of the expression by $\cos A$. This allows us to use the given value of $\tan A$, since $\tan A = \frac{\sin A}{\cos A}$.
Expression: $ \frac{\cos A - \sin A}{\cos A + \sin A} $
Divide numerator and denominator by $\cos A$:
$ \frac{\frac{\cos A}{\cos A} - \frac{\sin A}{\cos A}}{\frac{\cos A}{\cos A} + \frac{\sin A}{\cos A}} $Simplify using $\frac{\sin A}{\cos A} = \tan A$:
$ \frac{1 - \tan A}{1 + \tan A} $Substituting the Value of tan A
Now, substitute the given value $\tan A = \frac{3}{4}$ into the simplified expression:
$ \frac{1 - \frac{3}{4}}{1 + \frac{3}{4}} $Calculate the numerator and the denominator:
- Numerator: $1 - \frac{3}{4} = \frac{4}{4} - \frac{3}{4} = \frac{1}{4}$
- Denominator: $1 + \frac{3}{4} = \frac{4}{4} + \frac{3}{4} = \frac{7}{4}$
Now, perform the division:
$ \frac{\frac{1}{4}}{\frac{7}{4}} $To divide fractions, multiply by the reciprocal of the denominator:
$ \frac{1}{4} \times \frac{4}{7} = \frac{1}{7} $Thus, the value of the expression is $\frac{1}{7}$.
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 cos x = p/q and 0° < x < 90°, then the value of tan x is:
