$cosec 30 ° ⋅ tan 2 45 ° − sec 2 60 °$ = ____.

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Detailed Solution

cosec 30 ° ⋅ tan 2 45 ° − sec 2 60 ° = 0

.
Given expression is

c o s e c 2 30 ° . t a n 2 45 ° − sec 2 60 °

.
We know that,

cos e c 30 ° = 2

sec 60 ° = 2

tan 45 ° = 1

.
Putting the values in the expression, we get,

⇒ c o s e c 2 30 ° . t a n 2 45 ° − sec 2 60 ° = 22 × (1) 2 − 22

⇒ c o s e c 2 30 ° . t a n 2 45 ° − sec 2 60 ° = 4 × 1 − 4 ⇒ c o s e c 2 30 ° . t a n 2 45 ° − sec 2 60 ° = 4 − 4 ⇒ c o s e c 2 30 ° . t a n 2 45 ° − sec 2 60 ° = 0

Thus,

c o s e c 2 30 ° . t a n 2 45 ° s e c 2 60 ° = 0

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