Question

Sec 610°×cosec 160°-cot 380°×cot470°

Answer 1

Answer:

Step-by-step explanation:

sec610∘cosec160∘−cot380∘tan470∘

=sec(720∘−110∘)cosec(180∘−20∘)

−cot(360∘+20∘)tan(360∘+110∘)

=1cos110∘.1sin20∘−cot20∘tan110∘

=−1sin220∘+cot220∘

=−[cosec220∘−cot220∘]

=−1

Answer 2

sec610° × cosec160° - cot380° × tan470° = - 1

Given : ( Correct Question)

sec 610° × cosec 160° - cot 380° × tan 470°

To find : The value

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is

sec 610° × cosec 160° - cot 380° × tan 470°

Step 2 of 2 :

Find the value

sec 610° × cosec 160° - cot 380° × tan 470°

= sec (630° - 20°) × cosec (180° - 20°) - cot (360° + 20°) × tan (450° + 20°)

= sec (7 × 90° - 20°) × cosec (2 × 90° - 20°) - cot (4 × 90° + 20°) × tan (5 × 90° + 20°)

= - cosec 20° × cosec 20° - cot 20° × - cot 20°

= - cosec² 20° + cot² 20°

= - ( cosec² 20° - cot² 20° )

= - 1

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