Question

tanA = 1/2 tanB = 1/3 then cos2A​

Answer 1

$\tan(a) = \frac{1}{2}$

$squaring \: both \: the \: sides$

${tan}^{2}(a) = {( \frac{1}{2}) }^{2}$

$\ { \tan}^{2} (a) = \frac{1}{4}$

${\sec}^{2} (a ) - 1 = \frac{1}{4}$

${ \sec }^{2} (a) = \frac{1}{4} + 1$

$\ { \sec}^{2} (a) = \frac{5}{4}$

$taking \: square \: root \: on \: both \: sides$

$\sec(a) = \frac{ \sqrt{5} }{2}$

$\frac{1}{ \sec(a) } = \frac{2}{ \sqrt{5} }$

$\cos(a) = \frac{2}{ \sqrt{5}}$

⭐Hope it helps⭐

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