Question 25 of 42intermediate🔧 ApplyShort Answer3 marks

Find the values of each of the expressions: tan(sin⁻¹(3/5) + cot⁻¹(3/2))

Correct Answer

17/6

Exercise: EXERCISE 2.2 | Q: 12 | (Page 13)
For More Understanding

Explanation

This problem requires using the tangent addition formula after converting inverse trigonometric functions to their trigonometric ratios. The key insight is to express sin⁻¹(3/5) and cot⁻¹(3/2) as angles, then find their tangent values using right triangle definitions.

Solution Steps

  1. Step 1: Let sin⁻¹(3/5) = A, so sin A = 3/5. In a right triangle, opposite = 3, hypotenuse = 5, therefore adjacent = 25−9\sqrt{25-9} = 4. Hence, tan A = 3/4.

  2. Step 2: Let cot⁻¹(3/2) = B, so cot B = 3/2. Therefore, tan B = 2/3.

  3. Step 3: Using tan(A + B) = (tan A + tan B)/(1 - tan A · tan B), substitute the values.

  4. Step 4: tan(A + B) = (3/4 + 2/3)/(1 - 3/4 · 2/3) = (17/12)/(1 - 1/2) = (17/12)/(1/2) = 17/6.

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