Step 1: Find the value of sin θ. Given cos θ = 3/5. Using the Pythagorean identity sin² θ + cos² θ = 1: sin² θ + (3/5)² = 1; sin² θ + 9/25 = 1; sin² θ = 1 − 9/25; sin² θ = 25/25 − 9/25; sin² θ = 16/25 Taking the square root, we get: sin θ = ± √(16/25) = ± 4/5 Assuming θ is an acute angle (in the first quadrant), sin θ is positive. sin θ = 4/5 Step 2: Simplify tan(90° − θ). Using the complementary angle identity, tan(90° − θ) = cot θ. Step 3: Find the value of cot θ. We know that cot θ = (cos θ)/(sin θ). Substitute the values of cos θ and sin θ: cot θ = (3/5)/(4/5) = 3/4 Step 4: Substitute the values into the expression sin θ − tan(90° − θ). The expression becomes: sin θ − cot θ Substitute the values found in Step 1 and Step 3: 4/5 − 3/4 Step 5: Calculate the final value. To subtract the fractions, find a common denominator, which is 20: (4 × 4)/(5 × 4) − (3 × 5)/(4 × 5) 16/20 − 15/20 (16 − 15)/(20) 1/20 The final answer is: 1/20

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Given theta = (3)/(5).

April 24, 2026Mathematics

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Answer

\frac{1}{20}

Step-by-step solution

5 steps

Find the value of $\sin \theta$ .
Given $\cos \theta = \frac{3}{5}$ .
Using the Pythagorean identity $\sin^2 \theta + \cos^2 \theta = 1$ :
$\sin^2 \theta + \left(\frac{3}{5}\right)^2 = 1$ $\sin^2 \theta + \frac{9}{25} = 1$ $\sin^2 \theta = 1 - \frac{9}{25}$ $\sin^2 \theta = \frac{25}{25} - \frac{9}{25}$ $\sin^2 \theta = \frac{16}{25}$
Taking the square root, we get:
$\sin \theta = \pm \sqrt{\frac{16}{25}} = \pm \frac{4}{5}$
Assuming $\theta$ is an acute angle (in the first quadrant), $\sin \theta$ is positive.
$\sin \theta = \frac{4}{5}$
Simplify $\tan(90^\circ - \theta)$ .
Using the complementary angle identity, $\tan(90^\circ - \theta) = \cot \theta$ .
Find the value of $\cot \theta$ .
We know that $\cot \theta = \frac{\cos \theta}{\sin \theta}$ .
Substitute the values of $\cos \theta$ and $\sin \theta$ :
$\cot \theta = \frac{\frac{3}{5}}{\frac{4}{5}} = \frac{3}{4}$
Substitute the values into the expression $\sin \theta - \tan(90^\circ - \theta)$ .
The expression becomes:
$\sin \theta - \cot \theta$
Substitute the values found in Step 1 and Step 3:
$\frac{4}{5} - \frac{3}{4}$
Calculate the final value.
To subtract the fractions, find a common denominator, which is 20:
$\frac{4 \times 4}{5 \times 4} - \frac{3 \times 5}{4 \times 5}$ $\frac{16}{20} - \frac{15}{20}$ $\frac{16 - 15}{20}$ $\frac{1}{20}$

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Given theta = (3)/(5).

Answer

Step-by-step solution

Find the value of sin⁡θ\sin \thetasinθ.

Simplify tan⁡(90∘−θ)\tan(90^\circ - \theta)tan(90∘−θ).

Find the value of cot⁡θ\cot \thetacotθ.

Substitute the values into the expression sin⁡θ−tan⁡(90∘−θ)\sin \theta - \tan(90^\circ - \theta)sinθ−tan(90∘−θ).

Calculate the final value.

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More Mathematics Questions

Find the value of $\sin \theta$ .

Simplify $\tan(90^\circ - \theta)$ .

Find the value of $\cot \theta$ .

Substitute the values into the expression $\sin \theta - \tan(90^\circ - \theta)$ .