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What is \( \Large sin 25^{\circ} sin 35^{\circ} sec 65^{\circ} sec 55^{\circ}\) equal to?

A) -1
B) 0
C) \( \Large \frac{1}{2} \)
D) 1

Correct Answer:




D) 1

Description for Correct answer:

sin 25 \( ^{\circ}\) sin 35 \( ^{\circ}\) sec 65 \( ^{\circ}\) sec 55 \( ^{\circ}\)

=> \( \Large sin \ 25 ^{\circ} \ sin \ 35 ^{\circ} .\frac{1}{cos \ 65 ^{\circ} }.\frac{1}{cos \ 55 ^{\circ} } \)

=> \( \Large sin \ 25 ^{\circ} . \ sin \ 35 ^{\circ} \times \frac{1}{cos(90 ^{\circ} -25 ^{\circ} )} \times \frac{1}{cos(90 ^{\circ} -35 ^{\circ} )} \)

=> \( \Large sin \ 25 ^{\circ} \times sin \ 35 ^{\circ} \times \frac{1}{sin25 ^{\circ} } \times \frac{1}{sin35 ^{\circ} } \)

=> 1

Part of solved Trigonometry questions and answers : >> Elementary Mathematics >> Trigonometry

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