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NDA 2016 Maths · Mathematics · Trigonometric Functions and Identities · medium

The value of sin 105^°+cos 105^° is

Single correct option

The value of sin⁡105∘+cos⁡105∘\sin105^\circ+\cos105^\circ is
  1. A. 12\dfrac12
  2. B. 12\dfrac1{\sqrt2}
  3. C. 32\dfrac{\sqrt3}2
  4. D. 11
Show answer and solution

Answer: (B) 12\dfrac1{\sqrt2}

Write sin⁡θ+cos⁡θ=2sin⁡(θ+45∘)\sin\theta+\cos\theta=\sqrt2\sin(\theta+45^\circ). For θ=105∘\theta=105^\circ this is 2sin⁡150∘=2⋅12=12\sqrt2\sin150^\circ=\sqrt2\cdot\dfrac12=\dfrac1{\sqrt2}. Using the sum of the values sin⁡105∘=sin⁡75∘\sin105^\circ=\sin75^\circ and cos⁡105∘=−sin⁡15∘\cos105^\circ=-\sin15^\circ gives the same result; assuming both are positive would give a larger value.
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Original question written in the NDA 2016 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake