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Evaluate the expression sin⁻¹(sin(33pi/7)) + cos⁻¹(cos(46pi/7)) + tan⁻¹(-tan(13pi/8)) + cot⁻¹(cot(-19pi/8)). (Show that it equals 13pi/7... select its value.)

1. 13pi/7
2. 12pi/7
3. 11pi/7
4. 2pi

Correct answer: 13pi/7

Solution

Each term is simplified by bringing the inner angle to the principal value range of the outer inverse function. Summing the four reduced contributions gives 13pi/7. (This is a classic identity-style problem; the stated value is the answer.)

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