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the answer is 4
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EXPLANATION.
Value of :
⇒ sin3π/2 + cosecπ/6.
As we know that,
We can first find the value of 3π/2 and π/6.
⇒ 3π/2 = 3 x 180/2 = 3 x 90 = 270°.
⇒ π/6 = 180/6 = 30°.
We can write equation as,
⇒ sin(270°) + cosec(30°).
⇒ sin(180° + 90°) + cosec(30°).
⇒ - sin(90°) + cosec(30°).
⇒ - 1 + 2 = 1.
Option [D] is the correct answer.
MORE INFORMATION.
(1) = sin⁻¹x.
Domain = [-1,1].
Range = [-π/2, π/2].
(2) = cos⁻¹x.
Domain = [-1,1].
Range = [0,π].
(3) = tan⁻¹x.
Domain = (-∞, ∞).
Range = (-π/2, π/2).
(4) = cot⁻¹x.
Domain = (-∞, ∞).
Range = (0, π).
(5) = sec⁻¹x.
Domain = (-∞, -1] ∪ [1, ∞).
Range = [0, π/2) ∪ (π/2, π].
(6) = cosec⁻¹x.
Domain = (-∞, -1] ∪ [1, ∞).
Range = [-π/2, 0) ∪ (0, π/2].
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