Question

cot (-15π/4)+cosec (-1410)​

Answer 1

To find :

• we need to find the value of cot(-15π/4) + cosec (-1410)

Solution :

• cot(-15π/4) + cosec (-1410)

= -cot(15π/4) + cosec(-1410) [cot(-x) = -cot x]

= -cot[(16π - π)/4] + cosec (-1410 + 4 × 360)

= - cot(16π/4 - π/4) + cosec (-1410 + 1440)

= - cot(4π - π/4) + cosec 30°

= -cot(-π/4) + 2 [cosec 30° = 2]

= cot π/4 + 2

= cot 45 + 2

= 1 + 2 [cot 45° = 1 ]

= 3

Hence,

• value of cot(-15π/4) + cosec (-1410) = 3

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Some Identities :-

• cos²x + sin²x = 1
• 1 + tan²x = sec ²x
• 1 + cot²x = cosec x
• sin(-x) = -sin x
• cos(-x) = cos x
• tan(-x) = tan x

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