Question

if tan a is 3/4 then cos²a -sin²a​

Answer 1

        $\text{It is given that }tanA = \dfrac34$

        $\text{We must find }cos^2A - sin^2A$

        $\text{We know that }cos2x = cos^2x - sin^2x$

$\implies \text{We must find }cos2A$

        $\text{We also know that }cos2x = \dfrac{1-tan^2x}{1+tan^2x}$

$\implies \: cos2A = \dfrac{1-tan^2A}{1+tan^2A}$

$\implies \: cos2A = \dfrac{1-\dfrac{3^2}{4^2}}{1+\dfrac{3^2}{4^2}}$

$\implies \: cos2A = \dfrac{1-\dfrac{9}{16}}{1+\dfrac{9}{16}}$

$\implies \: cos2A = \dfrac{\dfrac{7}{16}}{\dfrac{25}{16}}$

$\implies \: cos2A = \dfrac{7}{25}$

$\implies \: \boxed{cos^2A - sin^2A = \dfrac{7}{25}}$