Question

cos 75° x sec 165° x sin 165°
sin 105° x tan 105° x cosec 105°​

Answer 1

SOLUTION

TO DETERMINE

The value of

cos 75° × sec 165° × sin 165° × sin 105° × tan 105° × cosec 105°

EVALUATION

cos 75° × sec 165° × sin 165° × sin 105° × tan 105° × cosec 105°

= cos 75° × sec ( 90° + 75° ) × sin ( 90° + 75° ) × sin ( 180° - 75°) × tan ( 180° - 75° ) × cosec ( 180° - 75° )

= cos 75° × - cosec 75° × cos 75° × sin 75° × - tan 75° × cosec 75°

$\displaystyle \sf{ = \cos {75}^{ \circ} \times \frac{1}{ \sin {75}^{ \circ} } \times \cos {75}^{ \circ} \times \sin {75}^{ \circ} \times \frac{\sin {75}^{ \circ}}{\cos {75}^{ \circ}} \times \frac{1}{\sin {75}^{ \circ}} }$

= sin 75°

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