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What is the value of $(cos 0 ∘ + sin 45 ∘ + sin 30 ∘) (sin 90 ∘ − cos 45 ∘ + cos 60 ∘)$ ?

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0

54

94

74

answer is D.

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Detailed Solution

Let the given be,

(cos 0 ∘ + sin 45 ∘ + sin 30 ∘) (sin 90 ∘ − cos 45 ∘ + cos 60 ∘)

… (1)
We know that,

sin 45 ∘ = 12 cos 45 ∘ = 12 sin 30 ∘ = 12 cos 60 ∘ = 12 cos 0 ∘ = 1 sin 90 ∘ = 1

Substitute the above values in the equation (1), we get
Question Image

Hence, the correct option is 4.

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