Question

If cos9 theta =sin theta and 9 theta<90° then find value of tan5 theta

Answer 1

Answer:

cos(9*theta) = cos(90° - theta)

9*theta = 90° - theta

10*theta = 90  --->  theta = 9°  --->  5*theta = 45°

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Answer 2

$\huge\underline\mathbb\red{Solution}$

$Given,\: cos9 \alpha = sin,\: \alpha\:and \: 9 \alpha < 90° \\i.e. \: \alpha\:is \: an \: acute \: angle. \\ sin(90° - 9 \alpha ) = sin\: \alpha \\{cos \: A \: = sin(90° - a)} \\ = > 90° - 9 \alpha = \alpha \\ = > 10 \alpha = 90° \\ = > \alpha = 9° \\ Therefore, \: tan5 \alpha = tan(5 \times 9)\:= tan45° \\ {tan45° = 1}$