What is the value of the expression (sec 30° + cos 60° + cot 45°)–(sin 30° + tan 45° – cosec60°) ?

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-1

2(1+

13

)

answer is D.

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Detailed Solution

Given expression is (sec 30° + cos 60° + cot 45°) – (sin 30° + tan 45° – cosec60°).
We know that,

cos x = sin (90 ∘ − x), cot x = tan (90 ∘ − x), and sec x = cos e c (90 ∘ − x)

sec 30 ° + cos 60 ° + cot 45 ° – cos 90 − 30 ° + cot 90 − 45 ° – sec 90 ° − 60 ° ⇒ sec 30 ° + cos 60 ° + cot 45 ° – cos 60 ° + cot 45 ° – sec 60 ° ⇒ sec 30 ° + cos 60 ° + cot 45 ° – cos 60 ° – cot 45 ° + sec 60 ° ⇒ sec 30 ° + sec 60 °

We know the values of secant of special angles,
sec(60°) = 2, sec(30°) =

23

.
Putting these in expression we get,
= 2+

23

= 2(1+

13

)
The value of the expression (sec 30° + cos 60° + cot 45°) – (sin 30° + tan 45° – cosec60°) is

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