Use the cofunction identities to evaluate the expression below without the aid of a calculator. $\cos ^ { 2 } 50 ^ { \circ } + \cos ^ { 2 } 58 ^ { \circ } + \cos ^ { 2 } 40 ^ { \circ } + \cos ^ { 2 } 32 ^ { \circ }$
A) 1
B) 2
C) $- 1$
D) 0
E) $\frac { 1 } { 2 }$

Question

Quizplus · Accepted Answer

The cofunction identities state that $\sin(\theta) = \cos(90^\circ - \theta)$ and $\cos(\theta) = \sin(90^\circ - \theta)$. Therefore, $\cos^2(50^\circ) = \sin^2(40^\circ)$ and $\cos^2(58^\circ) = \sin^2(32^\circ)$. The given expression simplifies to $\sin^2(40^\circ) + \sin^2(32^\circ) + \cos^2(40^\circ) + \cos^2(32^\circ)$. Since $\sin^2(\theta) + \cos^2(\theta) = 1$, the expression simplifies to $1 + 1 = 2$.

Use the Cofunction Identities to Evaluate the Expression Below Without cos⁡250∘+cos⁡258∘+cos⁡240∘+cos⁡232∘\cos ^ { 2 } 50 ^ { \circ } + \cos ^ { 2 } 58 ^ { \circ } + \cos ^ { 2 } 40 ^ { \circ } + \cos ^ { 2 } 32 ^ { \circ }cos250∘+cos258∘+cos240∘+cos232∘

Use the Cofunction Identities to Evaluate the Expression Below Without $\cos ^ { 2 } 50 ^ { \circ } + \cos ^ { 2 } 58 ^ { \circ } + \cos ^ { 2 } 40 ^ { \circ } + \cos ^ { 2 } 32 ^ { \circ }$