Question

56. If cos 8a = sin a and 8a < 90°, then the value of
4 tan 6a ishi whae ​

Answer 1

Answer:

$4 \tan(6a) = \frac{4}{ \sqrt{3} }$

Explanation:

$\cos(8a) = \: \sin(a ) \\ so \: \: \: \cos(8a) = \cos( {90}^{o} - a ) \: \: \: \: [since \: sin \alpha = \cos( {90}^{o} - \alpha) ] \\ so \: \: \: 8a = {90}^{o} - a \\ so \: \: \: 9a = {90}^{o} \\ so \: \: \: a = {10}^{o} \\ \\ \\ now \: \: 4 \tan(6a) = 4 \tan(6 \times {10}^{o} ) = 4 \tan( {60}^{o} ) \\ \: \: \: \: \: \: \: \: \: \: = 4 \times \frac{1}{ \sqrt{3} } = \frac{4}{ \sqrt{3} }$

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