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Evaluate the expression cot⁻¹(cosec⁻¹(5/3) + tan⁻¹(2/3)).

1. 6/17
2. 3/17
3. 4/17
4. 5/17

Correct answer: 6/17

Solution

cosec^-1(5/3) is an angle A with sin A=3/5, so tan A=3/4; tan B=2/3. tan(A+B)=(3/4+2/3)/(1-(3/4)(2/3))=(17/12)/(1/2)=17/6. Hence cot(A+B)=6/17.

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