Use the cofunction identities to evaluate the expression without using a calculator. $$\tan ^ { 2 } 61 + \cot ^ { 2 } 18 - \sec ^ { 2 } 72 - \csc ^ { 2 } 29$$
A) $- 2$
B) 3
C) $- 1$
D) 1
E) 2

Question

Use the cofunction identities to evaluate the expression without using a calculator. $$\tan ^ { 2 } 61 + \cot ^ { 2 } 18 - \sec ^ { 2 } 72 - \csc ^ { 2 } 29$$ 
A) $- 2$
B) 3
C) $- 1$
D) 1
E) 2

Quizplus · Accepted Answer

The correct answer is A because $\tan ^ { 2 } 61 = \cot ^ { 2 } 29$ and $\cot ^ { 2 } 18 = \tan ^ { 2 } 72$. So, the expression simplifies to $\tan ^ { 2 } 61 + \cot ^ { 2 } 18 - \sec ^ { 2 } 72 - \csc ^ { 2 } 29 = \cot ^ { 2 } 29 + \tan ^ { 2 } 72 - \sec ^ { 2 } 72 - \csc ^ { 2 } 29 = 0 - 1 = -1$.

Use the Cofunction Identities to Evaluate the Expression Without Using tan⁡261+cot⁡218−sec⁡272−csc⁡229\tan ^ { 2 } 61 + \cot ^ { 2 } 18 - \sec ^ { 2 } 72 - \csc ^ { 2 } 29tan261+cot218−sec272−csc229

Use the Cofunction Identities to Evaluate the Expression Without Using $\tan ^ { 2 } 61 + \cot ^ { 2 } 18 - \sec ^ { 2 } 72 - \csc ^ { 2 } 29$