If m + 5 = sec²A cosec²A (1 - cos²A)(1 - sin²A) + 5, then find the value of m.

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Accepted Answer

Given: m + 5 = sec²A * cosec²A * (1 - cos²A) * (1 - sin²A) + 5

Step 1: Use trigonometric identities:
1 - cos²A = sin²A
1 - sin²A = cos²A

Step 2: Substitute these in the expression:
sec²A * cosec²A * sin²A * cos²A + 5

Step 3: Recall that:
sec A = 1/cos A => sec²A = 1/cos²A
cosec A = 1/sin A => cosec²A = 1/sin²A

Step 4: Substitute sec²A and cosec²A:
(1/cos²A) * (1/sin²A) * sin²A * cos²A + 5

Step 5: Simplify:
(1/cos²A) * (1/sin²A) * sin²A * cos²A = 1

So, m + 5 = 1 + 5 = 6

Step 6: Therefore, m = 6 - 5 = 1

Hence, the value of m is 1.

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