Question

Find the exact value of the expression-

$1-{\cos }^{2}20°-{\cos }^{2}70°$

Short answer

The required value is,

$1-{\cos }^{2}20°-{\cos }^{2}70°=0$

Step-by-step solution

Step 1. Given information

Given expression

$1-{\cos }^{2}20°-{\cos }^{2}70°$

Step 2. Calculation

Solving the given expression,

$$\begin{gathered} 1-{\cos }^{2}20°-{\cos }^{2}70° \\ ={\sin }^{2}20°-{\cos }^{2}70° \end{gathered}$$ ---------$\{\left({\sin }^2\theta +{\cos }^2\theta \right)=1\}$

localid="1647102453546" $$\begin{gathered} ={\sin }^2\left(90°-70°\right)-{\cos }^{2}70° \\ ={\cos }^{2}70°-{\cos }^{2}70° \\ =0 \end{gathered}$$ ----------$\{\sin \left(90°-\theta \right)=\cos \theta \}$