Question

The value of the expression ${\text{cos}}^2\text{23°-}{\sin }^2\text{67°}$ is positive .

• A. True
• B. False

Answer 1

The correct option is B False

In this question we use the formula ${\text{(a}}^2{\text{-b}}^2\text{)=(a-b)(a+b)}$

Here ${\text{cos}}^2{\text{23°-sin}}^2\text{67°=(cos23°-sin67°)(cos23°+sin67°)}$

We know that $\text{sin(90-θ)=cosθ}$

$$\begin{gathered} \text{(cos23°-sin(90-23°))(cos23°+sin(90-23°)} \\ =\text{(cos23°-cos23°)(cos23°+cos23°)} \\ =\left(0\right)(2\text{cos23°)=0} \end{gathered}$$

And $0$ is neither positive nor negative.

Hence, the given statement is a false statement.