Find the exact value of the expression. Do not use a calculator.
-$1 + \sin ^ { 2 } 85 ^ { \circ } + \sin ^ { 2 } 5 ^ { \circ }$
A) 2
B) 0
C) -1
D) 1 )1

Question

Quizplus · Accepted Answer

The identity $\sin^2 \theta + \cos^2 \theta = 1$ can be used here, noting that $\sin^2 85^\circ = \cos^2 5^\circ$ because $\sin 85^\circ = \cos (90^\circ - 85^\circ) = \cos 5^\circ$. Therefore, $1 + \sin^2 85^\circ + \sin^2 5^\circ = 1 + \cos^2 5^\circ + \sin^2 5^\circ = 1 + 1 = 2$.

Find the Exact Value of the Expression 1+sin⁡285∘+sin⁡25∘1 + \sin ^ { 2 } 85 ^ { \circ } + \sin ^ { 2 } 5 ^ { \circ }1+sin285∘+sin25∘

Find the Exact Value of the Expression $1 + \sin ^ { 2 } 85 ^ { \circ } + \sin ^ { 2 } 5 ^ { \circ }$