Find the value of (7)/(3 x 2) + (1)/(6)

March 22, 2026Mathematics

ScanSolve AI Answer

March 22, 2026

Answer

\dfrac{5}{13}

Step 1: Given $\sin A = \frac{12}{13}$ , use the identity $\sin^2 A + \cos^2 A = 1$ .

\sin^2 A + \cos^2 A = 1

Step 2: Substitute $\sin A = \frac{12}{13}$ .

\cos^2 A = 1 - \left( \frac{12}{13} \right)^2

Step 3: Compute $\left( \frac{12}{13} \right)^2$ .

\left( \frac{12}{13} \right)^2 = \frac{144}{169}

Step 4: Simplify.

\cos^2 A = 1 - \frac{144}{169} = \frac{169}{169} - \frac{144}{169} = \frac{25}{169}

Step 5: Solve for $\cos A$ .

\cos A = \pm \sqrt{\frac{25}{169}} = \pm \frac{5}{13}

Assuming acute angle, $\cos A = \frac{5}{13}$ .

\dfrac{5{13}}

Step 1: Given $\cos B = \frac{3}{5}$ , use the identity $\sin^2 B + \cos^2 B = 1$ .

\sin^2 B + \cos^2 B = 1

Step 2: Substitute $\cos B = \frac{3}{5}$ .

\sin^2 B = 1 - \left( \frac{3}{5} \right)^2

Step 3: Compute $\left( \frac{3}{5} \right)^2$ .

\left( \frac{3}{5} \right)^2 = \frac{9}{25}

Step 4: Simplify.

\sin^2 B = 1 - \frac{9}{25} = \frac{25}{25} - \frac{9}{25} = \frac{16}{25}

Step 5: Solve for $\sin B$ .

\sin B = \pm \sqrt{\frac{16}{25}} = \pm \frac{4}{5}

Assuming acute angle, $\sin B = \frac{4}{5}$ .

\dfrac{4{5}}

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Quick Answer

Given A = (12)/(13), use the identity ^2 A + ^2 A = 1. ^2 A + ^2 A = 1 Step 2: Substitute A = (12)/(13).

Asked on March 22, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on March 22, 2026

Step 1: Given A = (12)/(13), use the identity ^2 A + ^2 A = 1. ^2 A + ^2 A = 1 Step 2: Substitute A = (12)/(13). ^2 A = 1 - ( (12)/(13) )^2 Step 3: Compute ( (12)/(13) )^2. ( (12)/(13) )^2 = (144)/(169) Step 4: Simplify. ^2 A = 1 - (144)/(169) = (169)/(169) - (144)/(169) = (25)/(169) Step 5: Solve for A. A = ± sqrt((25)/(169)) = ± (5)/(13) Assuming acute angle, A = (5)/(13). (5)/(13) Step 1: Given B = (3)/(5), use the identity ^2 B + ^2 B = 1. ^2 B + ^2 B = 1 Step 2: Substitute B = (3)/(5). ^2 B = 1 - ( (3)/(5) )^2 Step 3: Compute ( (3)/(5) )^2. ( (3)/(5) )^2 = (9)/(25) Step 4: Simplify. ^2 B = 1 - (9)/(25) = (25)/(25) - (9)/(25) = (16)/(25) Step 5: Solve for B. B = ± sqrt((16)/(25)) = ± (4)/(5) Assuming acute angle, B = (4)/(5). (4)/(5)